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Graph with all vertices of degree 3
of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are
Cubic_graph
Cubic graph with 10 vertices and 15 edges
problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no
Petersen_graph
Polynomial function of degree 3
{b}{3a}}.} The graph of a cubic function is a cubic curve, though many cubic curves are not graphs of functions. Although cubic functions depend on
Cubic_function
Constructs with triply-connected vertices
The connected 3-regular (cubic) simple graphs are listed for small vertex numbers. The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices
Table_of_simple_cubic_graphs
Undirected graph with 14 vertices
field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and all
Heawood_graph
Fewest edge crossings in drawing of a graph
graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is
Crossing number (graph theory)
Crossing_number_(graph_theory)
Type of crystal structure
coordinatization of the diamond cubic involves the removal of some of the edges from a three-dimensional grid graph. In this coordinatization, which
Diamond_cubic
Family of cubic graphs formed from regular and star polygons
In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding
Generalized_Petersen_graph
Unproven conjecture in graph theory
mathematics Must every cubic graph contain a simple cycle of length a power of two? More unsolved problems in mathematics In graph theory, the unproven
Erdős–Gyárfás_conjecture
Distance-transitive cubic graph with 20 nodes and 30 edges
In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after
Desargues_graph
Cubic graph with 28 vertices and 42 edges
field of graph theory, the Coxeter graph is a 3-regular graph with 28 vertices and 42 edges. It is one of the 13 known cubic distance-regular graphs. It is
Coxeter_graph
Graph in which all ordered pairs of linked nodes are automorphic
Other well known cubic symmetric graphs are the Dyck graph, the Foster graph and the Biggs–Smith graph. The ten distance-transitive graphs listed above,
Symmetric_graph
3-regular graph with no 3-edge-coloring
needed for the edges of a cubic graph is either three ("class one" graphs) or four ("class two" graphs), so snarks are cubic graphs of class two. However
Snark_(graph_theory)
Graphs formed by a hypercube's edges and vertices
cubic graphs, which are graphs that have exactly three edges touching each vertex. The only hypercube graph Q n {\displaystyle Q_{n}} that is a cubic
Hypercube_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
Archimedean solid with 8 faces
It has 12 vertices and 18 edges. It is a connected cubic graph, and connected cubic transitive graph. As a Wythoff construction, it is vertex transitive
Truncated_tetrahedron
Undirected cubic graph with 12 vertices and 18 edges
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz
Tietze's_graph
Cubic graph with 8 vertices and 12 edges
3-edge-connected. The Wagner graph has 392 spanning trees; it and the complete bipartite graph K3,3 have the most spanning trees among all cubic graphs with the same
Wagner_graph
Length of a shortest cycle contained in the graph
The Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is the unique 6-cage, the McGee graph is the unique
Girth_(graph_theory)
Topics referred to by the same term
= 0) Cubic form, a homogeneous polynomial of degree 3 Cubic graph (mathematics - graph theory), a graph where all vertices have degree 3 Cubic plane
Cubic
Cubic graph with 12 vertices and 18 edges
In graph theory, the Frucht graph is a cubic graph with 12 vertices, 18 edges, and no nontrivial symmetries. It was first described by Robert Frucht in
Frucht_graph
3-regular graph with 30 vertices and 45 edges
the unique smallest cubic graph of girth 8, it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized
Tutte–Coxeter_graph
Mathematical puzzle of avoiding crossings
Thomsen. It is a well-covered graph, the smallest triangle-free cubic graph, and the smallest non-planar minimally rigid graph. A review of the history of
Three_utilities_problem
Symmetric bipartite cubic graph with 16 vertices and 24 edges
In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August
Möbius–Kantor_graph
unit distance graphs Jaeger's Petersen-coloring conjecture: every bridgeless cubic graph has a cycle-continuous mapping to the Petersen graph The list coloring
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mapping a graph onto itself without changing edge-vertex connectivity
automorphism group of a connected graph – indeed, of a cubic graph. Constructing the automorphism group of a graph, in the form of a list of generators
Graph_automorphism
24-vertex symmetric bipartite cubic graph
In the mathematical field of graph theory, the Nauru graph is a symmetric, bipartite, cubic graph with 24 vertices and 36 edges. It was named by David
Nauru_graph
Mathematical graph theorem
follows: Petersen's Theorem. Every cubic, bridgeless graph contains a perfect matching. In other words, if a graph has exactly three edges at each vertex
Petersen's_theorem
Path in a graph that visits each vertex exactly once
notation for Hamiltonian cubic graphs. Lovász conjecture that vertex-transitive graphs are Hamiltonian Pancyclic graph, graphs with cycles of all lengths
Hamiltonian_path
Graph able to be embedded on a torus
the mathematical field of graph theory, a toroidal graph is a graph that can be embedded on a torus. In other words, the graph's vertices and edges can be
Toroidal_graph
Concept in graph theory
showed in 2008 that it is NP-complete to determine whether a semi-cubic graph (a graph where every vertex has degree 1 or 3) is 4-incidence colorable. This
Incidence_(graph)
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
Two special graphs in graph theory
orientable surface of genus 3, in which they form dual graphs. This is a 3-regular (cubic) graph with 56 vertices and 84 edges, named after Felix Klein
Klein_graphs
Polynomial equation of degree 3
Consequently, the roots of the equation in t sum to zero. When the graph of a cubic function is plotted in the Cartesian plane, if there is only one real
Cubic_equation
number 3, chromatic index 3, girth 4 and diameter 8. The Tutte graph is a cubic polyhedral graph, but is non-hamiltonian. Therefore, it is a counterexample
Tutte_graph
Bipartite, 3-regular undirected graph
configuration. All the cubic, distance-regular graphs are known; the Pappus graph is one of the 13 such graphs. The Pappus graph has rectilinear crossing
Pappus_graph
Graph with a prism as its skeleton
vertex transitive cubic graphs, and bipartite graphs (also called bicubic graphs). A 4-crossed prism graph is the same as the cubical graph with 8 vertices
Prism_graph
Cycle graph with all opposite nodes linked
vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of M6 (the utility graph K3,3), Mn has exactly n/2 four-cycles
Möbius_ladder
In the mathematical field of graph theory, the F26A graph is a symmetric bipartite cubic graph with 26 vertices and 39 edges. It has chromatic number 2
F26A_graph
Planar, undirected graph with 2n vertices and 3n-2 edges
called prism graphs. Circular ladder graphs: Connecting the four 2-degree vertices of a standard ladder graph crosswise creates a cubic graph called a Möbius
Ladder_graph
Graph with a triangular truncated trapezohedron as its skeleton
ranging from 72° to 82°. The Dürer graph is the graph formed by the vertices and edges of the Dürer solid. It is a cubic graph of girth 3 and diameter 4. As
Dürer_graph
Undirected graph with no non-trivial symmetries
there are infinitely many asymmetric cubic graphs. The class of asymmetric graphs is closed under complements: a graph G is asymmetric if and only if its
Asymmetric_graph
Graph with 24 vertices and 36 edges
smallest cubic graph of girth 7). It is also the smallest cubic cage that is not a Moore graph. First discovered by Sachs but unpublished, the graph is named
McGee_graph
Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Hofman Graph H(12
List_of_graphs
mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches
Gray_graph
Disproven graph theory
mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices".
Tait's_conjecture
Branch of mathematics
graphs can be drawn up. By Frucht's theorem, all groups can be represented as the automorphism group of a connected graph (indeed, of a cubic graph)
Algebraic_graph_theory
Graph where each vertex has the same number of neighbors
or 4-regular graph often is called a cubic graph or a quartic graph, respectively. Similarly, it is possible to denote k-regular graphs with k = 5 , 6
Regular_graph
counterexample to the Tutte conjecture that every cubic 3-connected bipartite graph is Hamiltonian. After the Horton graph, a number of smaller counterexamples to
Horton_graph
Cycles in a graph that cover each edge twice
cycle of the original graph, or to a pair of cycles meeting at v. Thus, every minimal counterexample must be cubic. But if a cubic graph can have its edges
Cycle_double_cover
Archimedean solid with 14 faces
vertices and 36 edges, and is a cubic Archimedean graph. It has book thickness 3 and queue number 2. As a Hamiltonian cubic graph, it can be represented by
Truncated_octahedron
Semi-symmetric cubic graph with 110 vertices and 165 edges
110-vertex Iofinova–Ivanov graph is, in graph theory, a semi-symmetric cubic graph with 110 vertices and 165 edges. The graph is named after Marina Evgenievna
110-vertex Iofinova–Ivanov graph
110-vertex_Iofinova–Ivanov_graph
Regular graph with 70 nodes and 105 edges
3-edge-connected, non-planar, cubic graph. It has book thickness 3 and queue number 2. The characteristic polynomial of the Harries graph is ( x − 3 ) ( x − 1
Harries_graph
Graph with only one possible coloring
uniquely 3-edge-colorable graphs that do not fit into this classification, such as the graph of the triangular pyramid. If a cubic graph is uniquely 3-edge-colorable
Uniquely_colorable_graph
Largest independent set of paired elements
applies to cubic graphs, graphs with exactly three edges incident to each vertex. It forms a new graph with each vertex and edge of the given graph replaced
Matroid_parity_problem
Unsolved problem in graph theory
every cubic bipartite polyhedral graph Hamiltonian? More unsolved problems in mathematics Barnette's conjecture is an unsolved problem in graph theory
Barnette's_conjecture
Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De
List_of_graph_theory_topics
Mathematical tree with cycle through leaves
Halin graph, with the tree inside it. Halin graphs are named after German mathematician Rudolf Halin, who studied them in 1971. The cubic Halin graphs – the
Halin_graph
Graph made from vertices and edges of a convex polyhedron
the Tutte embedding. Tait conjectured that every cubic polyhedral graph (that is, a polyhedral graph in which each vertex is incident to exactly three
Polyhedral_graph
Embedding a graph in a topological space, often Euclidean
graph-encoded map, an edge-colored cubic graph with four vertices for each edge of the embedded graph. The problem of finding the graph genus is NP-hard (the problem
Graph_embedding
Graph with equal-size maximal independent sets
characterizations of the well-covered cubic graphs, well-covered claw-free graphs, and well-covered graphs of high girth allow these graphs to be recognized in polynomial
Well-covered_graph
Undirected bipartite graph with 112 vertices and 168 edges
in 2002 and named after Ljubljana (the capital of Slovenia). It is a cubic graph with diameter 8, radius 7, chromatic number 2 and chromatic index 3.
Ljubljana_graph
Polyhedron resembling a soccerball
Archimedean graph because it resembles one of the Archimedean solids. It is a cubic graph, meaning that each vertex is incident to exactly three edges. The balls
Truncated_icosahedron
Archimedean solid with 14 faces
solids. It has 24 vertices and 36 edges, and is a cubic Archimedean graph. As a Hamiltonian cubic graph, it can be represented by LCF notation as LCF[2
Truncated_cube
Undirected cubic graph derived from a hypercube graph
In graph theory, the cube-connected cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle. It was introduced
Cube-connected_cycles
Periodic spatial graph
maximal abelian covering graph of the three-edge dipole graph, and the diamond cubic is the maximal abelian covering graph of the four-edge dipole. The
Laves_graph
Edge whose deletion would disconnect a graph
Analogously to bridgeless graphs being 2-edge-connected, graphs without articulation vertices are 2-vertex-connected. In a cubic graph, every cut vertex is
Bridge_(graph_theory)
Concept in graph theory
a cubic graph has a K-flow if and only if it is 3-edge-colorable. As a corollary a cubic graph that is 3-edge colorable is 4-face colorable. A graph is
Nowhere-zero_flow
Representation of a graph as a path graph "thickened" by some amount
In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number
Pathwidth
Graph where all pairs of vertices are automorphic
cubic vertex-transitive graphs on at most 1280 vertices. Although every Cayley graph is vertex-transitive, there exist other vertex-transitive graphs
Vertex-transitive_graph
Decomposition of a graph into hamiltonion cycles
In graph theory, a branch of mathematics, a Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles
Hamiltonian_decomposition
Graph that is edge-transitive and regular but not vertex-transitive
possible cubic semi-symmetric graphs after the Gray graph are the Iofinova–Ivanov graph on 110 vertices, the Ljubljana graph on 112 vertices, a graph on 120
Semi-symmetric_graph
Five-pointed star polygon
space Pentalpha – Puzzle involving stones and a pentagram Petersen graph – Cubic graph with 10 vertices and 15 edges Ptolemy's theorem – Relates the 4 sides
Pentagram
Assignment of colors to edges of a graph
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color
Edge_coloring
3-edge-connected non-planar cubic graph. It has book thickness 3 and queue number 2. The characteristic polynomial of the Harries–Wong graph is ( x − 3 ) ( x −
Harries–Wong_graph
Infinite family of graphs
Isaacs in 1975. As snarks, the flower snarks are connected, bridgeless cubic graphs with chromatic index equal to 4. The flower snarks are non-planar and
Flower_snark
Unproven generalization of the four-color theorem
in mathematics Does every graph with chromatic number k {\displaystyle k} have a k {\displaystyle k} -vertex complete graph as a minor? More unsolved
Hadwiger conjecture (graph theory)
Hadwiger_conjecture_(graph_theory)
Representation of cubic graphs
extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle. The cycle itself includes two out of
LCF_notation
Every graph has evenly many odd vertices
odd vertices in an appropriate "exchange graph". For instance, as C. A. B. Smith proved, in any cubic graph G {\displaystyle G} there must be an even
Handshaking_lemma
Graph invariant defined from axis-parallel unit cubes
field of graph theory, cubicity is a graph invariant defined to be the smallest dimension such that a graph can be realized as the intersection graph of axis-parallel
Cubicity
Natural number
independent sets in a four-dimensional (16 vertex) hypercube graph, and exactly 743 connected cubic graphs with 16 vertices and girth four. Sloane, N. J. A. (ed
743_(number)
Geometry with 7 points and 7 lines
particular graph is a connected cubic graph (regular of degree 3), has girth 6 and each part contains 7 vertices. It is the Heawood graph, the unique
Fano_plane
In graph theory, a quotient graph Q of a graph G is a graph whose vertices are blocks of a partition of the vertices of G and where block B is adjacent
Quotient_graph
Solid with six equal square faces
drawing a graph with vertices connected with an edge in a plane. Such a graph is called the cubical graph, a special case of the hypercube graph. The cube
Cube
Representation of a mathematical function
{\displaystyle \{a,b,c,d\}} , however, cannot be determined from the graph alone. The graph of the cubic polynomial on the real line f ( x ) = x 3 − 9 x {\displaystyle
Graph_of_a_function
Non-Hamiltonian simple polyhedron
graph theory, the Barnette–Bosák–Lederberg graph is a cubic (that is, 3-regular) polyhedral graph with no Hamiltonian cycle, the smallest such graph possible
Barnette–Bosák–Lederberg graph
Barnette–Bosák–Lederberg_graph
Problem of finding a cycle through all vertices of a graph
theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly
Hamiltonian_path_problem
every cubic 3-connected bipartite graph is Hamiltonian. The book thickness of the Ellingham-Horton 54-graph and the Ellingham-Horton 78-graph is 3 and
Ellingham–Horton_graph
Graph where all pairs of edges are automorphic
edge-transitive graph that is also regular, but still not vertex-transitive, is called semi-symmetric. The Gray graph, a cubic graph on 54 vertices, is
Edge-transitive_graph
be less than 165, see Wolfram MathWorld. The Tutte 12-cage is a cubic Hamiltonian graph and can be defined by the LCF notation [17, 27, −13, −59, −35,
Tutte_12-cage
Visualization of node-link graphs
of a graph is the minimum number of distinct edge slopes needed in a drawing with straight line segment edges (allowing crossings). Cubic graphs have
Graph_drawing
Bipartite 3-regular graph with 90 vertices and 135 edges
census of cubic symmetric graphs included this graph. The bipartite half of the Foster graph is a distance-regular graph and a locally linear graph. It is
Foster_graph
On Hamiltonian cycles in planar graphs
non-Hamiltonicity of some counterexamples to Tait's conjecture that cubic polyhedral graphs are Hamiltonian. Grinberg's theorem is named after Latvian mathematician
Grinberg's_theorem
Graph describing a topological embedding
rotation systems and ribbon graphs. The graph-encoded map for an embedded graph G {\displaystyle G} is another cubic graph H {\displaystyle H} together
Graph-encoded_map
Graph without four-vertex star subgraphs
In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the
Claw-free_graph
Cubic distance-regular graph with 102 nodes and 153 edges
3-vertex-connected graph and a 3-edge-connected graph. All the cubic distance-regular graphs are known. The Biggs–Smith graph is one of the 13 such graphs. The automorphism
Biggs–Smith_graph
Geometric configuration of 9 points and 9 lines
pairs of points. The Levi graph of the Pappus configuration is known as the Pappus graph. It is a bipartite symmetric cubic graph with 18 vertices and 27
Pappus_configuration
American mathematician (1898–1965)
shows that six colours may be needed is the 12-vertex cubic graph now known as the Franklin graph. Franklin also worked with Jay W. Forrester on Project
Philip_Franklin
Dejter graph admits a 3-factorization into two copies of the Ljubljana graph, which is the third smallest existing semi-symmetric cubic graph of regular
Dejter_graph
Scottish mathematical physicist (1831–1901)
mathematical discipline. His name is known in graph theory mainly for Tait's conjecture on cubic graphs. He is also one of the namesakes of the Tait–Kneser
Peter_Guthrie_Tait
CUBIC GRAPH
CUBIC GRAPH
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
English (North Midlands)
English (North Midlands) : unexplained; possibly a dialect variant of Cubit, but see also Cuppett.
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
English
English : from Middle English cubit ‘forearm’ (from Latin cubitum), presumably applied as a nickname for someone with strong or otherwise remarkable forearms; in its extended sense, as a unit of length, it may have been a metonymic occupational name for a builder.
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...
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).
Surname or Lastname
English
English : variant spelling of Cubit.
CUBIC GRAPH
CUBIC GRAPH
Boy/Male
English
Birch valley; birch tree meadow.
Girl/Female
Hindu, Indian
The Gods Ornament
Boy/Male
Russian
noble.
Girl/Female
Arabic, Australian, British, English, Muslim
Fine Silk Brocade
Girl/Female
Assamese, Indian
Very Beautiful
Female
Japanese
(å¤å) Japanese name NATSUKO means "summer child."
Girl/Female
Muslim
Sweet. Pleasant.
Girl/Female
Assamese, Bengali, Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Tamil, Telugu, Traditional
Love; Affectionate; Wife of Rishi Sandeep; Friendly
Girl/Female
Hindu, Indian, Kannada, Marathi, Sindhi, Telugu
Sweet Voice Like a Cuckoo Bird
Boy/Male
Indian, Sanskrit
Lamp Like; Luminous; Radiant
CUBIC GRAPH
CUBIC GRAPH
CUBIC GRAPH
CUBIC GRAPH
CUBIC GRAPH
n.
The tenth part of the stere or cubic meter, equal to 3.531 cubic feet. See Stere.
n.
A measure of length, being the distance from the elbow to the extremity of the middle finger.
a.
Of or pertaining to the pubes; in the region of the pubes; as, the pubic bone; the pubic region, or the lower part of the hypogastric region. See Pubes.
a.
A pile of wood containing 108 cubic feet.
n.
A cubic measure containing 1000 cubic meters, and equivalent to 35,315 cubic feet.
n.
A curve of the third degree.
a.
See Cufic.
n.
A titanate of lime occurring in octahedral or cubic crystals.
a.
See Cuming.
a.
Of or pertaining to the older characters of the Arabic language.
a.
Isometric or monometric; as, cubic cleavage. See Crystallization.
n.
A measure of capacity in the metric system, being a cubic decimeter, equal to 61.022 cubic inches, or 2.113 American pints, or 1.76 English pints.
n.
A liter, or cubic decimeter.
n.
A measure of solidity, containing one hundred cubic meters, and equivalent to 3531.66 English or 3531.05 United States cubic feet.
n.
A unit of cubic measure in the metric system, being a cubic meter, or kiloliter, and equal to 35.3 cubic feet, or nearly 1/ cubic yards.
n.
The pubic bone.
n.
The forearm; the ulna, a bone of the arm extending from elbow to wrist.
a.
Of or pertaining to the pubis.
n.
A measure of capacity equal to a cubic meter, or a thousand liters. It is equivalent to 35.315 cubic feet, and to 220.04 imperial gallons, or 264.18 American gallons of 321 cubic inches.
a.
Alt. of Cubical