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Graph representing a permutation
the mathematical field of graph theory, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent
Permutation_graph
the forbidden permutation patterns 2413 and 3142; they are also the permutations whose permutation graphs are cographs and the permutations that realize
Separable_permutation
Graph with tight clique-coloring relation
sequence and its permutation. The complement of a permutation graph is another permutation graph, for the reverse of the given permutation. Therefore, as
Perfect_graph
Class of artificial neural networks
designed to be permutation equivariant: reordering the nodes in the input reorders the corresponding node representations in the same way. For graph-level prediction
Graph_neural_network
Task of computing complete subgraphs
of graphs as well. For instance, in a circle graph, the neighborhood of each vertex is a permutation graph, so a maximum clique in a circle graph can
Clique_problem
Matrix with exactly one 1 per row and column
entries 0. An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM
Permutation_matrix
unconstrained permutations. Every permutation defines a permutation graph, a graph whose vertices are the elements of the permutation and whose edges
Stack-sortable_permutation
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
Graph representing intersections between given sets
notion of permutation graph, in turn they are a special case of the family of the complements of comparability graphs known as cocomparability graphs. A unit
Intersection_graph
Type of permutation of a set of elements
is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has
Derangement
Non-crossing graph with vertices on outer face
dihedral permutation of its outer cycle. Chartrand and Harary also proved an analogue of Kuratowski's theorem for outerplanar graphs, that a graph is outerplanar
Outerplanar_graph
Graph linking pairs of comparable elements in a partial order
intervals. Therefore, permutation graphs are another subclass of comparability graphs. The trivially perfect graphs are the comparability graphs of rooted trees
Comparability_graph
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
Pair of positions in a sequence where two elements are out of sorted order
that are out of their natural order. Let π {\displaystyle \pi } be a permutation. There is an inversion of π {\displaystyle \pi } between i {\displaystyle
Inversion (discrete mathematics)
Inversion_(discrete_mathematics)
Intersection graph for intervals on the real number line
comparability graph, it follows that graph and its complement are both interval graphs if and only if the graph is both a split graph and a permutation graph. The
Interval_graph
Graph with oriented edges
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed
Directed_graph
Mapping a graph onto itself without changing edge-vertex connectivity
edge–vertex connectivity. Formally, an automorphism of a graph G = (V, E) is a permutation σ of the vertex set V, such that the pair of vertices (u,
Graph_automorphism
permutation is skew-merged if and only if its associated permutation graph is a split graph, a graph that can be partitioned into a clique (corresponding
Skew-merged_permutation
Mathematical version of an order change
In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or
Permutation
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 corresponding
Trapezoid_graph
Graph where all pairs of vertices are automorphic
of graph theory, an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped to non-edges. A graph is
Vertex-transitive_graph
Graph formed by complementation and disjoint union
special cases of the distance-hereditary graphs, permutation graphs, comparability graphs, and perfect graphs. Any cograph may be constructed using the
Cograph
Computer science problem
largest clique in a permutation graph corresponds to the longest decreasing subsequence of the permutation that defines the graph (assuming the original
Longest increasing subsequence
Longest_increasing_subsequence
Subpermutation of a longer permutation
theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation
Permutation_pattern
Polynomial in combinatorial mathematics
complete graph K3 is isomorphic to its own line graph (vertex-edge dual) and hence the edge permutation group induced by the vertex permutation group is
Cycle_index
Permutation graph Permutation pattern Permutation polynomial Permutohedron Rencontres numbers Robinson–Schensted correspondence Sum of permutations:
List_of_permutation_topics
Intersection graph of a chord diagram
circle graphs as a special case. Every distance-hereditary graph is a circle graph, as is every permutation graph and every indifference graph. Every
Circle_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
Matrix representation of a graph
In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian
Laplacian_matrix
Two-sided graph with consecutive neighbors
forward-convex graphs are equivalent to permutation graphs. A biconvex graph is forward-convex (and hence a bipartite permutation graph) if and only if
Convex_bipartite_graph
Mathematical measure for partial orders
comparability graphs of the partial orders of dimension two are exactly the permutation graphs, graphs that are both themselves comparability graphs and complementary
Order_dimension
Number of vertices with unambiguous distances
interval graphs, and more generally to graphs of bounded tree-length, such as chordal graphs, permutation graphs or asteroidal-triple-free graphs. Deciding
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
String in combinatorial math
finding superpermutations lies in creating a graph where each permutation is a vertex and every permutation is connected by an edge. Each edge has a weight
Superpermutation
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
Polyhedron whose vertices represent permutations
vertices of the Cayley graph are the inverse permutations of those in the permutohedron. The image on the right shows the Cayley graph of S4. Its edge colors
Permutohedron
Graph which partitions into a clique and independent set
permutation graphs are exactly the interval graphs that have interval graph complements; these are the permutation graphs of skew-merged permutations
Split_graph
Type of group in abstract algebra
groups of graphs, such as the Higman–Sims group and the Higman–Sims graph. The elements of the symmetric group on a set X are the permutations of X. The
Symmetric_group
vertices of the graph are considered to be labeled in such a way as to be distinguishable from each other, while in other problems any permutation of the vertices
Graph_enumeration
Type of permutation in combinatorial mathematics
In combinatorial mathematics, a Stirling permutation of order k is a permutation of the multiset 1, 1, 2, 2, ..., k, k (with two copies of each value
Stirling_permutation
Graphs formed by a hypercube's edges and vertices
In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the
Hypercube_graph
Graph with only one possible coloring
In graph theory, a uniquely colorable graph is a k-chromatic graph that has only one possible (proper) k-coloring up to permutation of the colors. Equivalently
Uniquely_colorable_graph
Probability distribution on equally likely outcomes
random permutation is a permutation generated uniformly randomly from the permutations of a given set and a uniform spanning tree of a graph is a spanning
Discrete_uniform_distribution
Geometry with 7 points and 7 lines
permutation 21 permutations with two 2-cycles 42 permutations with a 4-cycle and a 2-cycle 56 permutations with two 3-cycles The 48 permutations with a complete
Fano_plane
Index of articles associated with the same name
codes closed under cyclic permutations Cyclic convolution, a method of combining periodic functions Cycle decomposition (graph theory) Cycle decomposition
Cyclic_(mathematics)
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
Undirected graph with no non-trivial symmetries
it has no nontrivial symmetries. Formally, an automorphism of a graph is a permutation p of its vertices with the property that any two vertices u and
Asymmetric_graph
Task in computational graph theory
form of a graph may also be described as a permutation of its vertices. Canonical forms of a graph are also called canonical labelings, and graph canonization
Graph_canonization
classes: Interval graphs are precisely the graphs that are both chordal and AT-free. Permutation graphs are AT-free. Trapezoid graphs are AT-free. Cocomparability
Asteroidal_triple-free_graph
Tool for working with matrices
graph GX of X. Find a perfect matching in GX, corresponding to a positive permutation set in X. Let z[i] > 0 be the smallest entry in the permutation
Birkhoff_algorithm
In graph theory, the arrangement graph A n , k {\displaystyle A_{n,k}} is a graph defined on the vertex set consisting of all permutations of k {\displaystyle
Arrangement_graph
update sequence is a permutation one frequently speaks of a permutation SDS to emphasize this point. Example: Let Y be the circle graph on vertices {1,2,3
Graph_dynamical_system
Branch of discrete mathematics
examples of what is now known as Hamiltonian cycles in certain Cayley graphs on permutations. During the Renaissance, together with the rest of mathematics and
Combinatorics
tree? Szymanski's conjecture: every permutation on the n {\displaystyle n} -dimensional doubly-directed hypercube graph can be routed with edge-disjoint
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
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
Generalization of graph theory
{\displaystyle G} if the permutation is the identity. One then writes H ≅ G {\displaystyle H\cong G} . Note that all strongly isomorphic graphs are isomorphic,
Hypergraph
Graph drawing with vertices in horizontal layers
Layered graph drawing or hierarchical graph drawing is a type of graph drawing in which the vertices of a directed graph are drawn in horizontal rows or
Layered_graph_drawing
Square matrix used to represent a graph or network
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether
Adjacency_matrix
Concept in graph theory
the mathematical field of graph theory, the pancake graph Pn or n-pancake graph is a graph whose vertices are the permutations of n symbols from 1 to n
Pancake_graph
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
transitively on the graph's vertices. In other words, the graph has an automorphism which is a cyclic permutation of its vertices. The graph has an adjacency
Circulant_graph
Combinatorial representation of a graph on an orientable surface
of darts; σ is a permutation on D; α is an involution on D with no fixed point. Intuitively, a combinatorial map corresponds to a graph where each edge
Combinatorial_map
Polynomial that permutes a ring
In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g
Permutation_polynomial
Graph where every connected induced subgraph has a universal vertex
subset of the other. They are the permutation graphs defined from stack-sortable permutations. They are the graphs with the property that in each of its
Trivially_perfect_graph
Construction in combinatorial group theory
theory, the Schreier coset graph is a graph associated with a group G, a generating set of G, and a subgroup of G. The Schreier graph encodes the abstract structure
Schreier_coset_graph
problem in mathematics Can every permutation on the n {\displaystyle n} -dimensional doubly directed hypercube graph be routed with edge-disjoint paths
Szymanski's_conjecture
corresponding to the identity permutation. Moreover, G → n , k + 1 {\displaystyle {\overrightarrow {G}}_{n,k+1}} is the directed line graph of G → n , k {\displaystyle
Shift_graph
7-regular undirected graph with 50 nodes and 175 edges
the edges and on the arcs of the graph. Therefore, the Hoffman–Singleton graph is a symmetric graph. As a permutation group on 50 symbols, it can be generated
Hoffman–Singleton_graph
Statement in mathematical combinatorics
its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. As
Ramsey's_theorem
Conjecture in group theory
connected distance-transitive graphs having degree greater than 2. Sims, Charles C. (1967). "Graphs and finite permutation groups". Mathematische Zeitschrift
Sims_conjecture
Representation of a graph as a path graph "thickened" by some amount
the complements of chordal graphs, for permutation graphs, for cographs, for circular-arc graphs, for the comparability graphs of interval orders, and of
Pathwidth
Class of error correction codes
discussed above. Using the connection between permutation codes and independent sets in certain graphs one can improve the Gilbert–Varshamov bound asymptotically
Permutation_code
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Discrete mathematics decomposition
rectangulations and permutations and representations of planar graphs in three dimensions. Similar to bijections between rectangulations and permutation classes in
Rectangulations
3-regular graph with 30 vertices and 45 edges
Tutte–Coxeter graph is a symmetric graph; it has a group of 1440 automorphisms, which may be identified with the automorphisms of the group of permutations on six
Tutte–Coxeter_graph
Sliding puzzle with fifteen pieces and one space
exceptional graph on 7 vertices, it is possible to obtain all permutations unless the graph is bipartite, in which case exactly the even permutations can be
15_puzzle
Index of articles associated with the same name
Josephus permutation Ordered selections and partitions of the twelvefold way in combinatorics Ordered set, a bijection, cyclic order, or permutation Weak
Order_(mathematics)
Mathematical abelian group
group of permutations of these three elements, that is, the symmetric group S 3 {\displaystyle S_{3}} . The Klein four-group's permutations of its own
Klein_four-group
Natural number
In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: K5, the complete graph with
5
Independent set which is not a subset of any other independent set
-W.; Chen, G.-H. (1993), "Generate all maximal independent sets in permutation graphs", Internat. J. Comput. Math., 47 (1–2): 1–8, doi:10.1080/00207169308804157
Maximal_independent_set
other edge, making the Higman–Sims graph an edge-transitive graph. The outer elements induce odd permutations on the graph. As mentioned above, there are
Higman–Sims_graph
Type of router for integrated circuits
movable. In recent years, area routers have in general taken over. Permutation graph Feller, A. 1976. Automatic layout of low-cost quick-turnaround random-logic
Channel_routing
Least-weight tree connecting graph vertices
possible permutations of the edge weights. The number of such permutations is at most (r2)!. For each permutation, solve the MST problem on the given graph using
Minimum_spanning_tree
Branch of mathematics that studies the properties of groups
group as a permutation group, acting on itself (X = G) by means of the left regular representation. In many cases, the structure of a permutation group can
Group_theory
Type of permutation
combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set {1, 2, 3, ..., n} is a permutation (arrangement) of those numbers so
Alternating_permutation
In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. The study
Rank_3_permutation_group
proof relies on Cayley graphs, in particular, circulant graphs, and many of their decompositions come from the action of a permutation on a fixed subgraph
Cycle decomposition (graph theory)
Cycle_decomposition_(graph_theory)
In the mathematics of permutations, a layered permutation is a permutation that reverses contiguous blocks of elements. Equivalently, it is the direct
Layered_permutation
Mathematics problem
of the permutation. Every permutation can be decomposed into disjoint cycles, that is, cycles which have no common elements. The permutation of the first
100_prisoners_problem
Study of graphs defined by geometric means
partial cube is the skeleton of the permutohedron, a graph in which vertices represent permutations of a set of ordered objects and edges represent swaps
Geometric_graph_theory
Systematic classification of 12 related enumerative problems concerning two finite sets
concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number
Twelvefold_way
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
is a permutation matrix, then it constitutes a graph isomorphism. Fractional isomorphism is the coarsest of several different relaxations of graph isomorphism
Fractional_graph_isomorphism
Measure of graph complexity
of bipartite permutation graphs is unbounded (based on similar grid structure). Based on the characterization of cographs as the graphs with no induced
Clique-width
Recursively splitting a graph into subsets of nodes
on graphs, such as recognizing and transitively orienting comparability graphs, recognizing and finding permutation representations of permutation graphs
Modular_decomposition
Topics referred to by the same term
group, a group generated by a single element Cyclic permutation, a basic permutation (all permutations are products of cycles) Cycle (angular unit), a unit
Cycle
Bipartite non-Hamiltonian polyhedral graph
In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the
Herschel_graph
Concept in group theory
remains open. Babai, László; Seress, Ákos (1992), "On the diameter of permutation groups", European Journal of Combinatorics, 13 (4): 231–243, arXiv:1109
Diameter_(group_theory)
In combinatorial mathematics, a Baxter permutation is a permutation σ ∈ S n {\displaystyle \sigma \in S_{n}} which satisfies the following generalized
Baxter_permutation
Isomorphism of an object to itself
\mathbb {O} } ) is the exceptional Lie group G2. In graph theory an automorphism of a graph is a permutation of the nodes that preserves edges and non-edges
Automorphism
Combinatorial algorithm
labeled by the inverse permutation to the permutation defined by its vertex coordinates, the resulting labeling describes a Cayley graph of the symmetric group
Steinhaus–Johnson–Trotter algorithm
Steinhaus–Johnson–Trotter_algorithm
Sporadic simple group
the Hall–Janko group J2. It happens that J2 acts as a permutation group on the Hall–Janko graph of 100 points, the stabilizer of one point being a subgroup
Higman–Sims_group
PERMUTATION GRAPH
PERMUTATION GRAPH
Boy/Male
Hindu, Indian, Jain, Marathi, Sanskrit, Sindhi, Tamil
Lines on Any Particular Raaga from Sanskrit; Permutations and Combinations of Parents; Aarya Cost King Ashoka's Birth
Girl/Female
Hindu
Achievement, Omnipresence, Permeation
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
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).
Girl/Female
Tamil
Vyaapti | வà¯à®¯à®¾à®ªà®¤à¯€
Achievement, Omnipresence, Permeation
Vyaapti | வà¯à®¯à®¾à®ªà®¤à¯€
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Spanish American Italian Latin
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
PERMUTATION GRAPH
PERMUTATION GRAPH
Boy/Male
Tamil
Ramakant | ரமாகாஂத
Lord Vishnu
Boy/Male
Arabic, Muslim
Distinction of the Religion Islam
Boy/Male
Indian
Sri shankaracharya, Founder of Adwaitha philosophy
Girl/Female
Teutonic
From the town.
Female
Italian
Italian form of Latin Marcia, MARZIA means "defense" or "of the sea."
Boy/Male
American, British, English
Swordsman; Germanic Tribe; From Saxonny
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit
Life Giver
Girl/Female
Gujarati, Hindu, Indian, Tamil
Vine in a Beautiful Art
Girl/Female
Muslim/Islamic
Light
Boy/Male
Muslim
Reward
PERMUTATION GRAPH
PERMUTATION GRAPH
PERMUTATION GRAPH
PERMUTATION GRAPH
PERMUTATION GRAPH
n.
The quality or state of being graphic.
adv.
In a graphic manner; vividly.
n.
Long continuance.
a.
Pertaining to, containing, derived from, or resembling, graphite.
a.
Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer.
n.
The act of permeating, passing through, or spreading throughout, the pores or interstices of any substance.
n.
Any one of such possible arrangements.
a.
Resembling graphite or plumbago.
n.
The arrangement of any determinate number of things, as units, objects, letters, etc., in all possible orders, one after the other; -- called also alternation. Cf. Combination, n., 4.
n.
Alt. of Perduration
v. t.
Alteration in the order of a series; permutation.
a.
Proof against penetration or permeation by water; impervious to water; as, a waterproof garment; a waterproof roof.
a.
Alt. of Graphitoidal
n.
Permutation.
n.
See Graphoscope.
n.
Alt. of Graphicalness
n.
The substitution of one root vowel for another, thus indicating a corresponding modification of use or meaning; vowel permutation; as, get, gat, got; sing, song; hang, hung.
n.
The act of drinking excessively; a drinking bout.
n.
The act of permuting; exchange of the thing for another; mutual transference; interchange.
n.
Barter; exchange.