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Intersection graph for intervals on the real number line
In graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line, with a vertex for each interval and an edge
Interval_graph
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Class of problems in computer science
throughput. It is equivalent to finding a maximum independent set in an interval graph. A generalization of the problem considers k > 1 {\displaystyle k>1}
Interval_scheduling
Graph with tight clique-coloring relation
triangulated graphs, comparability graphs, proper interval graphs, proper circular-arc graphs, and nested interval graphs". Journal of Graph Theory. 6 (3):
Perfect_graph
Intersection graph of a chord diagram
set of intervals on a line is called the interval graph. String graphs, the intersection graphs of curves in the plane, include circle graphs as a special
Circle_graph
All numbers between two given numbers
(geometry) Inequality Interval graph Interval finite element Interval (statistics) Line segment Partition of an interval Unit interval Bertsekas, Dimitri
Interval_(mathematics)
Unrelated vertices in graphs
3-edge-colorable graphs is APX-complete. An interval graph is a graph in which the nodes are 1-dimensional intervals (e.g. time intervals) and there is an
Independent set (graph theory)
Independent_set_(graph_theory)
In graph theory, the interval chromatic number χ < ( H ) {\displaystyle \chi _{<}(H)} of an ordered graph H {\displaystyle H} is the minimum number of
Interval_coloring
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Graph representing intersections between given sets
intersection graph of intervals on the real line, or of connected subgraphs of a path graph. An indifference graph may be defined as the intersection graph of unit
Intersection_graph
Graph where all long cycles have a chord
decomposition of a graph is also the junction tree of the junction tree algorithm. Interval graphs are the intersection graphs of subtrees of path graphs, a special
Chordal_graph
Representation of a graph as a path graph "thickened" by some amount
given graph is a subgraph. Interval graphs are a special case of chordal graphs, and chordal graphs can be represented as intersection graphs of subtrees
Pathwidth
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Computer compiler optimization technique
Using liveness analysis, an interference graph can be built. The interference graph, which is an Interval graph where the nodes are the program's variables
Register_allocation
comparability graph of an interval order ( X {\displaystyle X} , ≤) is the interval graph ( X , ∩ ) {\displaystyle (X,\cap )} . Interval orders should
Interval_order
Graph without four-vertex star subgraphs
claw-free graphs. The complement of any triangle-free graph is claw-free. These graphs include as a special case any complete graph. Proper interval graphs, the
Claw-free_graph
graph Dense graph Dipole graph Directed acyclic graph Directed graph Distance regular graph Distance-transitive graph Edge-transitive graph Interval graph
List_of_graph_theory_topics
Longest distance between two vertices
be computed in linear time for interval graphs, and in near-linear time for graphs of bounded treewidth. In median graphs, the diameter can be found in
Diameter_(graph_theory)
Unsolved problem in computational complexity theory
Planar graphs (In fact, planar graph isomorphism is in log space, a class contained in P) Interval graphs Permutation graphs Circulant graphs Bounded-parameter
Graph_isomorphism_problem
In graph theory, a tolerance graph is an undirected graph in which every vertex can be represented by a closed interval and a real number called its tolerance
Tolerance_graph
Intersection graph of unit intervals on the real line
of interval representations, these graphs are also called unit interval graphs or proper interval graphs; they form a subclass of the interval graphs. A
Indifference_graph
Topics referred to by the same term
measurement Interval estimate Interval (graph theory) Space-time interval, the distance between two points in 4-space Intermission, (British English: interval),
Interval
Adjacent subset of an undirected graph
graph all of whose induced subgraphs have the property that any maximal clique intersects any maximal independent set in a single vertex. An interval
Clique_(graph_theory)
Graph which partitions into a clique and independent set
split graph and an interval graph, then its complement is both a split graph and a comparability graph, and vice versa. The split comparability graphs, and
Split_graph
Intersection graph for a set of arcs on a circle
recognition algorithm. Circular-arc graphs are a natural generalization of interval graphs. If a circular-arc graph G has an arc model that leaves some
Circular-arc_graph
Graphical representation of a computer program or algorithm
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during
Control-flow_graph
When every path in a control-flow graph must go through one node to reach another
postdominate any other strict postdominators of n. Control-flow graph Interval (graph theory) Static single assignment form Lengauer, Thomas; Tarjan,
Dominator_(graph_theory)
Number of vertices with unambiguous distances
bounded-degree planar graphs, split graphs, bipartite graphs and their complements, line graphs of bipartite graphs, unit disk graphs, interval graphs of diameter
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
"NP-completeness of the problem of finding a minimum-clique-number interval graph containing a given graph as a subgraph". Proceedings. International Symposium on
List_of_NP-complete_problems
Intersection graph of trapezoids between parallel lines
co-comparability graphs that contain interval graphs and permutation graphs as subclasses. A graph is a trapezoid graph if there exists a set of trapezoids
Trapezoid_graph
Graph linking pairs of comparable elements in a partial order
cocomparability graphs is self-complementary in the sense that the complement of a cocomparability graph is a comparability graph, and vice versa. Interval graphs are
Comparability_graph
outerplanar graphs. There is a constant-factor approximation algorithm for interval graphs and for bipartite graphs. The interval graph case remains
Sum_coloring
In mathematics, an object whose endomorphisms are isomorphic to another structure
graphs and circle orders", SIAM Journal on Discrete Mathematics, 4 (3): 448–451, doi:10.1137/0404040, MR 1105950 Fishburn, Peter C. (1985), Interval Orders
Representation_(mathematics)
self-complementary graph, a block graph, a split graph, an interval graph, a claw-free graph, a 1-vertex-connected graph and a 1-edge-connected graph. A graph is bull-free
Bull_graph
Hypergraph representing intervals on real number lines
In graph theory, a d-interval hypergraph is a kind of a hypergraph constructed using intervals of real lines. The parameter d is a positive integer. The
D-interval_hypergraph
result is the same.) Graphs of sphericity 1 {\displaystyle 1} are known as unit interval graphs or indifference graphs. Graphs of sphericity 2 {\displaystyle
Sphericity_(graph_theory)
Study of graphs defined by geometric means
is a geometric graph. For instance, the intersection graph of line segments in one dimension is an interval graph; the intersection graph of unit disks
Geometric_graph_theory
Graph where every connected induced subgraph has a universal vertex
perfect graphs that every trivially perfect graph is also a cograph, a chordal graph, a Ptolemaic graph, an interval graph, and a perfect graph. The threshold
Trivially_perfect_graph
Chordal graph with the given graph as a subgraph
planar graphs. A graph G is an AT-free graph if and only if all of its minimal chordal completions are interval graphs. G is a claw-free AT-free graph if
Chordal_completion
Maximum number of colors obtainable by a greedy graph coloring algorithm
For interval graphs, the chromatic number and Grundy number are within a factor of 8 of each other. Testing whether the Grundy number of a given graph is
Grundy_number
Tree graph with all nodes within distance 1 from central path
They are the connected graphs of pathwidth one. They are the connected triangle-free interval graphs. They are n-vertex graphs whose adjacency matrices
Caterpillar_tree
Logical formulation of graph properties
the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences
Logic_of_graphs
Node labeling problem in graph theory
clique size in a proper interval supergraph of the given graph, chosen to minimize its clique size. For several families of graphs, the bandwidth φ ( G )
Graph_bandwidth
Data structure for permutations
matrix for the consecutive ones property, recognizing interval graphs, and determining whether a graph is planar. If all the leaves of a PQ tree are connected
PQ_tree
Smallest dimension where a graph can be represented as an intersection graph of boxes
representation of this graph as an intersection graph of seven intervals (one-dimensional boxes) on the real number line. This graph cannot be represented
Boxicity
A graph is AT-free if it contains no asteroidal triples. AT-free graphs provide a common generalization of several important graph classes: Interval graphs
Asteroidal_triple-free_graph
Representation of a mathematical function
In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle
Graph_of_a_function
Spanning tree minimizing sum of distances
input graph, and by searching among all trees with k {\displaystyle k} internal nodes. The minimum routing cost spanning tree of an unweighted interval graph
Minimum routing cost spanning tree
Minimum_routing_cost_spanning_tree
Data organization and storage formats
graph-based data structures are used in computer science and related fields: Graph Adjacency list Adjacency matrix Graph-structured stack Scene graph
List_of_data_structures
Mathematical model combining space and time
for the same time interval, positive intervals are always timelike. If s 2 {\displaystyle s^{2}} is negative, the spacetime interval is said to be spacelike
Spacetime
Recursively splitting a graph into subsets of nodes
permutation graphs, recognizing whether a graph is a cograph and finding a certificate of the answer to the question, recognizing interval graphs and finding
Modular_decomposition
Graph formed by adding isolated or universal vertices
In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:
Threshold_graph
Type of graph in mathematics and physics
associated with the interval [ 0 , ∞ ) {\displaystyle [0,\infty )} attached to a single vertex at x e = 0 {\displaystyle x_{e}=0} . A graph with one or more
Quantum_graph
Coloring in which edges are labeled by integers
In graph theory, interval edge coloring is a type of edge coloring in which edges are labeled by the integers in some interval, every integer in the interval
Interval_edge_coloring
Conjecture in graph theory
spanning trees in a graph Chromatic polynomial Being a perfect graph or an interval graph, or certain other subclasses of perfect graphs Both the reconstruction
Reconstruction_conjecture
Branch of the mathematical field of graph theory
of the unit interval [0,1] per edge, with the endpoints of these intervals glued together at vertices. In this view, embeddings of graphs into a surface
Topological_graph_theory
Uniform restraint of the change in functions
{\displaystyle \delta } such that function values over any function domain interval of the size δ {\displaystyle \delta } are as close to each other as we
Uniform_continuity
Fewest cliques covering a graph's edges
In the mathematical field of graph theory, the intersection number of a graph G = ( V , E ) {\displaystyle G=(V,E)} is the smallest number of elements
Intersection number (graph theory)
Intersection_number_(graph_theory)
Measure of branching complexity
pathwidth of an arbitrary undirected graph G may be defined as the smallest number w such that there exists an interval graph H containing G as a subgraph, with
Strahler_number
Mathematical set with an ordering
and an ideal of L. An interval in a poset P is a subset that can be defined with interval notation: For a ≤ b, the closed interval [a, b] is the set of
Partially_ordered_set
Curve along which a 3-D surface is at equal elevation
equal value to the state. It is a plane section of the three-dimensional graph of the function f ( x , y ) {\displaystyle f(x,y)} parallel to the ( x
Contour_line
Problem of finding the longest simple path for a given graph
weighted trees, on block graphs, on cacti, on bipartite permutation graphs, and on Ptolemaic graphs. For the class of interval graphs, an O ( n 4 ) {\displaystyle
Longest_path_problem
Real function with secant line between points above the graph itself
line segment between any two distinct points on the graph of the function lies above or on the graph of the function between the two points. Equivalently
Convex_function
Property of elements related by inequalities
Hoffman, A. J. (1964), "A characterization of comparability graphs and of interval graphs", Canadian Journal of Mathematics, 16: 539–548, doi:10.4153/CJM-1964-055-5
Comparability
Chordal graph where all cycles of even length have odd chords
chordal graphs, which in turn includes the cluster graphs as the 2-leaf powers. Another important subclass of strongly chordal graphs are interval graphs. In
Strongly_chordal_graph
Type of chart
A line chart or line graph, also known as curve chart, is a type of chart that displays information as a series of data points called 'markers' connected
Line_chart
Topological space arising from a usual graph
In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph G = ( E , V ) {\displaystyle G=(E,V)} by replacing
Graph_(topology)
Range to estimate an unknown parameter
According to frequentist inference, a confidence interval (CI) is a range of values which is likely to contain (in repeated sampling) the true value of
Confidence_interval
Number denoting a graph's closeness to a tree
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest
Treewidth
Theorem in mathematics
the whole interval. Geometrically, this means that at some point the tangent to the graph is parallel to the secant line through the interval's endpoints
Mean_value_theorem
Numerical invariant of graphs
In graph theory, the tree-depth of a connected undirected graph G {\displaystyle G} is a numerical invariant of G {\displaystyle G} , the minimum height
Tree-depth
Basic integral in elementary calculus
of the integral of a function on an interval. It defines the integral by approximating the region under the graph of a function by finite sums of areas
Riemann_integral
product dimension. A threshold graph is a dot product graph with positive t and dot product dimension 1. Every interval graph has dot product dimension at
Dot product representation of a graph
Dot_product_representation_of_a_graph
Algorithmically defined graph
In the study of graph algorithms, an implicit graph representation (or more simply implicit graph) is a graph whose vertices or edges are not represented
Implicit_graph
Operation in mathematical calculus
region bounded by the graph of the function f(x) = x {\textstyle {\sqrt {x}}} between x = 0 and x = 1, one can divide the interval into five pieces (0,
Integral
Type of chart
A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that
Bar_chart
Graphical representation of data
A chart (sometimes known as a graph) is a graphical representation for data and information visualization, in which "the data is represented by symbols
Chart
Partition-based graph traversal method
including the recognition of comparability graphs and interval graphs. An enumeration of the vertices of a graph is said to be a LexBFS ordering if it is
Lexicographic breadth-first search
Lexicographic_breadth-first_search
is the definition of the average velocity for that interval of time on the graph. If this interval is made to be infinitesimally small, such that Δ s
Motion_graphs_and_derivatives
Probability of survival beyond any specified time
F(t)} and probability density function f ( t ) {\displaystyle f(t)} on the interval [ 0 , ∞ ) {\displaystyle [0,\infty )} , then the survival function or reliability
Survival_function
Set system used in greedy optimization
F.} It is easy to see that a matroid is also an interval greedoid. Consider an undirected graph G. Let the ground set be the edges of G and the feasible
Greedoid
Relationship between derivatives and integrals
with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
(1980). "Linear Time Automorphism Algorithms for Trees, Interval Graphs, and Planar Graphs". SIAM Journal on Computing. 10 (1). Society for Industrial
Lexicographically minimal string rotation
Lexicographically_minimal_string_rotation
Canadian graph theorist
algorithms in graph theory and special classes of graphs, including cographs, permutation graphs, interval graphs, comparability graphs and their complements
Lorna_Stewart
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
"Signed graphs," Discrete Applied Mathematics 4, pp. 401–406. Fulkerson, D. R.; Gross, O. A. (1965). "Incidence matrices and interval graphs". Pacific
Unimodular_matrix
Graph where all odd cycles of length ≥ 5 has 2+ chords
Meyniel graphs contain the chordal graphs, the parity graphs, and their subclasses the interval graphs, distance-hereditary graphs, bipartite graphs, and
Meyniel_graph
Matching which covers every node of the graph
In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph G with edges E and vertices
Perfect_matching
Human mortality as a result of coronavirus disease 2019 (COVID-19)
WHO reports, tables, and spreadsheets. There are also maps and timeline graphs of daily and weekly deaths worldwide. 7,114,321 (updated 6 June 2026) confirmed
COVID-19_pandemic_deaths
Continuous function on an interval takes on every value between its values at the ends
{\displaystyle 1} to 2 {\displaystyle 2} . Over the interval, the set of function values has no gap, and the graph can be drawn without lifting a pencil from the
Intermediate_value_theorem
1990 book by Gerhard Ringel and Nora Hartsfield
algebraic graph theory and spectral graph theory, connectivity of a graph (or even biconnected components), Hall's marriage theorem, line graphs, interval graphs
Pearls_in_Graph_Theory
Exercise strategy
High-intensity interval training (HIIT) is a training protocol alternating short periods of intense or explosive anaerobic exercise with brief recovery
High-intensity interval training
High-intensity_interval_training
Intersection graph for curves in the plane
of interval graphs. Later, Sinden (1966) specified the same idea to electrical networks and printed circuits. The mathematical study of string graphs began
String_graph
Directed graph representing overlaps between sequences of symbols
In graph theory, an n-dimensional De Bruijn graph of m symbols is a directed graph representing overlaps between sequences of symbols. It has mn vertices
De_Bruijn_graph
Independent set which is not a subset of any other independent set
maximal-clique irreducible graphs include triangle-free graphs, bipartite graphs, and interval graphs. Cographs can be characterized as graphs in which every maximal
Maximal_independent_set
of order dimension of interval orders. The shift graph G n , 2 {\displaystyle G_{n,2}} is the line-graph of the complete graph K n {\displaystyle K_{n}}
Shift_graph
Task of computing complete subgraphs
graphs in which the number of cliques is polynomially bounded. These families include chordal graphs, complete graphs, triangle-free graphs, interval
Clique_problem
Theorem relating graph minors and topological embeddings
In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between
Graph_structure_theorem
Search algorithm finding the position of a target value within a sorted array
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position
Binary_search
NP-complete graph problem
solved in polynomial time on interval graphs, while the subtree isomorphism problem is NP-complete on proper interval graphs. Sysło, Maciej M. (1982), "The
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
Possible distances in a bar-joint system
, δ ) {\displaystyle \Phi _{f,l_{p}}^{d}(G,\delta )} is a single interval. A graph G {\displaystyle G} has an inherent convex Cayley configuration space
Cayley_configuration_space
INTERVAL GRAPH
INTERVAL GRAPH
Surname or Lastname
English and French
English and French : nickname for a handsome man (perhaps also ironically for an ugly one), from Old French beu, bel ‘fair’, ‘lovely’ (Late Latin bellus).Hungarian (Bél) : from the old secular Hungarian name Bél, or alternatively from bél ‘internal part’, probably an occupational name for a servant who worked in the household.Czech (BÄ›l) from Czech bÃlý ‘white’.
Male
Greek
(ἈπολλÏων) Greek name APOLLYÅŒN means "destroyer." In the New Testament bible, this is the name of the angel-prince of the infernal regions, the minister of death and author of havoc on earth. He is also known by the name AbaddÅn.
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Girl/Female
American, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Plucked Flower; Voice of Heart; Woman; Intellect; Behold of Any Beautiful Scene; Internal Beauty
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Muslim, Punjabi, Sikh, Sindhi, Telugu
Heart; Inner Beauty; Fame; Internal Nature; Wisdom
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Male
Greek
(á¾Î¹Î´Î·Ï‚) Greek name derived from the word aides, HAIDES means "unseen." In mythology, this is the name of the god of the underworld, brother of Zeus and husband of Persephone. In the Greek bible, Haides is associated with Orcus, the realm of the dead, the infernal regions where disembodied spirits live, a dark and dismal place in the depths of the earth. Only later was Haides described as the grave, death, and hell. Also spelled HadÄ“s.Â
Male
English
Anglicized form of Greek ApollyÅn, APOLLYON means "destroyer." In the New Testament bible, this is the name of the angel-prince of the infernal regions, the minister of death and author of havoc on earth. He is also known by the name Abaddon.
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
German (also Gräff), Dutch, and Jewish (Ashkenazic)
German (also Gräff), Dutch, and Jewish (Ashkenazic) : variant of Graf.English : metonymic occupational name for a clerk or scribe, from Anglo-Norman French grafe ‘quill’, ‘pen’ (a derivative of grafer ‘to write’, Late Latin grafare, from Greek graphein).
Boy/Male
Gujarati, Hindu, Indian, Kannada, Punjabi, Sanskrit, Sikh, Traditional
Protector of All; Protector of God Indra; Gods Friends
Boy/Male
Sikh
Protector of Indra, Variant of Inder
Surname or Lastname
Irish
Irish : reduced Anglicized form of either of two Gaelic names, Ó DuibhÃn ‘descendant of DuibhÃn’, a byname meaning ‘little black one’, or Ó DaimhÃn ‘descendant of DaimhÃn’, a byname meaning ‘fawn’, ‘little stag’. These are attenuated versions of Ó Dubháin and Ó Damháin, and are the phonetic origin of Anglicizations with an internal v (as opposed to w, as in Dewan, or monosyllabic forms with an o or u) (see Doane).English and French : nickname, of literal or ironic application, from Middle English, Old French devin, divin ‘excellent’, ‘perfect’ (Latin divinus ‘divine’).
Boy/Male
Spanish American Italian Latin
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Indian
Internal Cleanliness
INTERVAL GRAPH
INTERVAL GRAPH
Boy/Male
Hindu, Indian, Marathi
Illuminated
Boy/Male
Muslim
Girl/Female
Arabic, Muslim
Noble; Honoured; Distinguished
Boy/Male
American, Anglo, Australian, British, English, German, Shakespearean, Teutonic
Divine Ruler
Boy/Male
German Scottish
Red. Surname.
Girl/Female
Indian
Goddess of wealth, Goddess Lakshmi, A Raaga in hindustani classical music
Boy/Male
Hindu, Indian, Marathi, Tamil
Lord Shiva
Girl/Female
Hindu
Girl/Female
Hindu
Lover of God, Friend of God
Male
Native American
Native American Cheyenne name MANTOTOHPA means "four bears."
INTERVAL GRAPH
INTERVAL GRAPH
INTERVAL GRAPH
INTERVAL GRAPH
INTERVAL GRAPH
v. t.
To interpel.
a.
Pertaining to, or proceeding by, integration; as, the integral calculus.
a.
Inward; interior; being within any limit or surface; inclosed; -- opposed to external; as, the internal parts of a body, or of the earth.
a.
Internal.
n.
A space between things; a void space intervening between any two objects; as, an interval between two houses or hills.
n.
Alt. of Intervale
n.
Intervening space; interval.
n.
An interval.
a.
Pertaining to its own affairs or interests; especially, (said of a country) domestic, as opposed to foreign; as, internal trade; internal troubles or war.
a.
Of or pertaining to, resembling, or inhabiting, hell; suitable for hell, or to the character of the inhabitants of hell; hellish; diabolical; as, infernal spirits, or conduct.
n.
Difference in pitch between any two tones.
n.
Space of time between any two points or events; as, the interval between the death of Charles I. of England, and the accession of Charles II.
n.
Interval; intermission.
n.
A brief space of time between the recurrence of similar conditions or states; as, the interval between paroxysms of pain; intervals of sanity or delirium.
a.
Derived from, or dependent on, the thing itself; inherent; as, the internal evidence of the divine origin of the Scriptures.
n.
A small interval, less than any in actual practice, but used in the mathematical calculation of intervals.
n.
An interhyal ligament or cartilage.
n.
An interval of a fifth; also, a part sung with such intervals.
n.
An interval.
n.
An inhabitant of the infernal regions; also, the place itself.