# Category: Individual graphs

Robertson–Wegner graph
In the mathematical field of graph theory, the Robertson–Wegner graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Neil Robertson and Gerd Wegner. It is one of the four (5
Loupekine snarks
In the mathematical field of graph theory, the Loupekine snarks are two snarks, both with 22 vertices and 33 edges. The first Loupekine snark graph can be described as follows (using the SageMath's sy
Wagner graph
In the mathematical field of graph theory, the Wagner graph is a 3-regular graph with 8 vertices and 12 edges. It is the 8-vertex Möbius ladder graph.
Klein graphs
In the mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in the orientable surface of genus 3, in which they f
Brouwer–Haemers graph
In the mathematical field of graph theory, the Brouwer–Haemers graph is a 20-regular undirected graph with 81 vertices and 810 edges.It is a strongly regular graph, a distance-transitive graph, and a
Young–Fibonacci lattice
In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. An
McLaughlin graph
In the mathematical field of graph theory, the McLaughlin graph is a strongly regular graph with parameters (275,112,30,56), and is the only such graph. The group theorist Jack McLaughlin discovered t
Pappus graph
In the mathematical field of graph theory, the Pappus graph is a bipartite 3-regular undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration. It is named a
Truncated icosidodecahedron
In geometry, the truncated icosidodecahedron is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces. It has 62 faces:
26-fullerene graph
In the mathematical field of graph theory, the 26-fullerene graph is a polyhedral graph with V = 26 vertices and E = 39 edges. Its planar embedding has three hexagonal faces (including the one shown a
Dodecahedron
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahe
Gray graph
In the 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 exactly three edges. It was discover
Poussin graph
In graph theory, the Poussin graph is a planar graph with 15 vertices and 39 edges. It is named after Charles Jean de la Vallée-Poussin.
Sousselier graph
The Sousselier graph is, in graph theory, a hypohamiltonian graph with 16 vertices and 27 edges. It has book thickness 3 and queue number 2.
Order-zero graph
No description available.
Diamond graph
In the mathematical field of graph theory, the diamond graph is a planar, undirected graph with 4 vertices and 5 edges. It consists of a complete graph minus one edge. The diamond graph has radius 1,
Chang graphs
In the mathematical field of graph theory, the Chang graphs are a set of three 12-regular undirected graphs, each with 28 vertices and 168 edges. They are strongly regular, with the same parameters an
120-cell
In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called a C120, dodecaplex (short for "dodecahedral c
Petersen graph
In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many prob
Errera graph
In the mathematical field of graph theory, the Errera graph is a graph with 17 vertices and 45 edges. Alfred Errera published it in 1921 as a counterexample to Kempe's erroneous proof of the four colo
Hoffman graph
In the mathematical field of graph theory, the Hoffman graph is a 4-regular graph with 16 vertices and 32 edges discovered by Alan Hoffman. Published in 1963, it is cospectral to the hypercube graph Q
Meringer graph
In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer. It is one of the four (5,5)-cage graphs, the ot
Hoffman–Singleton graph
In the mathematical field of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with parameters (50,7,0,1
Octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equi
Sylvester graph
The Sylvester graph is the unique distance-regular graphwith intersection array .It is a subgraph of the Hoffman–Singleton graph.
Wong graph
In the mathematical field of graph theory, the Wong graph is a 5-regular undirected graph with 30 vertices and 75 edges. It is one of the four (5,5)-cage graphs, the others being the Foster cage, the
Tutte graph
In the mathematical field of graph theory, the Tutte graph is a 3-regular graph with 46 vertices and 69 edges named after W. T. Tutte. It has chromatic number 3, chromatic index 3, girth 4 and diamete
Berlekamp–Van Lint–Seidel graph
In graph theory, the Berlekamp–Van Lint–Seidel graph is a locally linear strongly regular graph with parameters . This means that it has 243 vertices, 22 edges per vertex (for a total of 2673 edges),
Tutte 12-cage
In the mathematical field of graph theory, the Tutte 12-cage or Benson graph is a 3-regular graph with 126 vertices and 189 edges named after W. T. Tutte. The Tutte 12-cage is the unique (3-12)-cage (
Herschel 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 graph of a convex polyhedron), and is the smal
Coxeter graph
In the mathematical 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 named after Harold Scott
Frucht graph
In the mathematical field of 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 1939. The Frucht graph
Tutte–Coxeter graph
In the mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage or Cremona–Richmond graph is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph
Golomb graph
In graph theory, the Golomb graph is a polyhedral graph with 10 vertices and 18 edges. It is named after Solomon W. Golomb, who constructed it (with a non-planar embedding) as a unit distance graph th
Dyck graph
In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It is Hamiltonian with 120 distinct Hamiltonian cycles. It h
Dürer graph
In the mathematical field of graph theory, the Dürer graph is an undirected graph with 12 vertices and 18 edges. It is named after Albrecht Dürer, whose 1514 engraving Melencolia I includes a depictio
Triangle graph
In the mathematical field of graph theory, the triangle graph is a planar undirected graph with 3 vertices and 3 edges, in the form of a triangle. The triangle graph is also known as the cycle graph a
Franklin graph
In the mathematical field of graph theory, the Franklin graph is a 3-regular graph with 12 vertices and 18 edges. The Franklin graph is named after Philip Franklin, who disproved the Heawood conjectur
Heawood graph
In the mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood.
Wells graph
The Wells graph is the unique distance-regular graphwith intersection array .. Its spectrum is. Its queue number is 3 and its upper bound on the book thickness is 5.
Suzuki graph
The Suzuki graph is a strongly regular graph with parameters . Its automorphism group has order 896690995200 and contains as a subgroup of order 2 the Suzuki sporadic group. It is named for Michio Suz
Chvátal graph
In the mathematical field of graph theory, the Chvátal graph is an undirected graph with 12 vertices and 24 edges, discovered by Václav Chvátal. It is triangle-free: its girth (the length of its short
Balaban 11-cage
In the mathematical field of graph theory, the Balaban 11-cage or Balaban (3,11)-cage is a 3-regular graph with 112 vertices and 168 edges named after Alexandru T. Balaban. The Balaban 11-cage is the
Brinkmann graph
In the mathematical field of graph theory, the Brinkmann graph is a 4-regular graph with 21 vertices and 42 edges discovered by Gunnar Brinkmann in 1992. It was first published by Brinkmann and Mering
Gosset graph
The Gosset graph, named after Thorold Gosset, is a specific regular graph (1-skeleton of the 7-dimensional 321 polytope) with 56 vertices and valency 27.
Nauru 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 Eppstein after the twelve-pointed star in the flag
Blanuša snarks
In the mathematical field of graph theory, the Blanuša snarks are two 3-regular graphs with 18 vertices and 27 edges. They were discovered by Yugoslavian mathematician Danilo Blanuša in 1946 and are n
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with probability one) by choosing independently at
Higman–Sims graph
In mathematical graph theory, the Higman–Sims graph is a 22-regular undirected graph with 100 vertices and 1100 edges. It is the unique strongly regular graph srg(100,22,0,6), where no neighboring pai
Truncated tetrahedron
In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges (of two types). It can be constructed by trunca
Icosahedron
In geometry, an icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi) 'twenty' and from Ancient Greek ἕδρα
Grötzsch graph
In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5. It is named after German mathematician Her
Holt graph
In graph theory, the Holt graph or Doyle graph is the smallest half-transitive graph, that is, the smallest example of a vertex-transitive and edge-transitive graph which is not also symmetric. Such g
Desargues graph
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 Girard Desargues, arises from several different co
Hall–Janko graph
In the mathematical field of graph theory, the Hall–Janko graph, also known as the Hall-Janko-Wales graph, is a 36-regular undirected graph with 100 vertices and 1800 edges. It is a rank 3 strongly re
Kittell graph
In the mathematical field of graph theory, the Kittell graph is a planar graph with 23 vertices and 63 edges. Its unique planar embedding has 42 triangular faces. The Kittell graph is named after Irvi
Barnette–Bosák–Lederberg graph
In the mathematical field of 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. It was disco
Foster cage
In the mathematical field of graph theory, the Foster cage is a 5-regular undirected graph with 30 vertices and 75 edges. It is one of the four (5,5)-cage graphs, the others being the Meringer graph,
Wiener–Araya graph
The Wiener–Araya graph is, in graph theory, a graph on 42 vertices with 67 edges. It is hypohamiltonian, which means thatit does not itself have a Hamiltonian cycle but every graph formed by removing
Meredith graph
In the mathematical field of graph theory, the Meredith graph is a 4-regular undirected graph with 70 vertices and 140 edges discovered by Guy H. J. Meredith in 1973. The Meredith graph is 4-vertex-co
Bidiakis cube
In the mathematical field of graph theory, the Bidiakis cube is a 3-regular graph with 12 vertices and 18 edges.
Livingstone graph
In the mathematical field of graph theory, the Livingstone graph is a distance-transitive graph with 266 vertices and 1463 edges. Its intersection array is {11,10,6,1;1,1,5,11}. It is the largest dist
Möbius–Kantor graph
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 Ferdinand Möbius and Seligmann Kantor. It can b
Clebsch graph
In the mathematical field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with 80 edges. The 80-edge gra
Harries–Wong graph
In the mathematical field of graph theory, the Harries–Wong graph is a 3-regular undirected graph with 70 vertices and 105 edges. The Harries–Wong graph has chromatic number 2, chromatic index 3, radi
Gewirtz graph
The Gewirtz graph is a strongly regular graph with 56 vertices and valency 10. It is named after the mathematician Allan Gewirtz, who described the graph in his dissertation.
Tietze's graph
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 Friedrich Tietze, who showed in 1910 that the Möbi
F26A graph
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, chromatic index 3, diameter 5, radius 5 and gir
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The
Szekeres snark
In the mathematical field of graph theory, the Szekeres snark is a snark with 50 vertices and 75 edges. It was the fifth known snark, discovered by George Szekeres in 1973. As a snark, the Szekeres gr
Goldner–Harary graph
In the mathematical field of graph theory, the Goldner–Harary graph is a simple undirected graph with 11 vertices and 27 edges. It is named after A. Goldner and Frank Harary, who proved in 1975 that i
Foster graph
In the mathematical field of graph theory, the Foster graph is a bipartite 3-regular graph with 90 vertices and 135 edges. The Foster graph is Hamiltonian and has chromatic number 2, chromatic index 3
Truncated icosahedron
In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons. It is the only one of these shap
Horton graph
In the mathematical field of graph theory, the Horton graph or Horton 96-graph is a 3-regular graph with 96 vertices and 144 edges discovered by Joseph Horton. Published by Bondy and Murty in 1976, it
Dejter graph
In the mathematical field of graph theory, the Dejter graph is a 6-regular graph with 112 vertices and 336 edges. The Dejter graph isobtained by deleting a copyof the Hamming code of length 7 from the
Butterfly graph
In the mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices and 6 edges. It can be constructed b
Schläfli graph
In the mathematical field of graph theory, the Schläfli graph, named after Ludwig Schläfli, is a 16-regular undirected graph with 27 vertices and 216 edges. It is a strongly regular graph with paramet
Utility graph
No description available.
M22 graph
The M22 graph, also called the Mesner graph or Witt graph is the unique strongly regular graph with parameters (77, 16, 0, 4). It is constructed from the Steiner system (3, 6, 22) by representing its
Moser spindle
In graph theory, a branch of mathematics, the Moser spindle (also called the Mosers' spindle or Moser graph) is an undirected graph, named after mathematicians Leo Moser and his brother William, with
Perkel graph
In mathematics, the Perkel graph, named after Manley Perkel, is a 6-regular graph with 57 vertices and 171 edges. It is the unique distance-regular graph with intersection array (6, 5, 2; 1, 1, 3). Th
Ljubljana graph
In the mathematical field of graph theory, the Ljubljana graph is an undirected bipartite graph with 112 vertices and 168 edges. It is a cubic graph with diameter 8, radius 7, chromatic number 2 and c
Markström graph
No description available.
Folkman graph
In the mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking every edge to every other edge,
Thomsen graph
No description available.
Robertson graph
In the mathematical field of graph theory, the Robertson graph or (4,5)-cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after Neil Robertson. The Robertson graph is the uniqu
Harborth graph
No description available.
Shrikhande graph
In the mathematical field of graph theory, the Shrikhande graph is a named graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices and 48 edges, with each vertex
Walther graph
In the mathematical field of graph theory, the Walther graph, also called the Tutte fragment, is a planar bipartite graph with 25 vertices and 31 edges named after Hansjoachim Walther. It has chromati
Biggs–Smith graph
In the mathematical field of graph theory, the Biggs–Smith graph is a 3-regular graph with 102 vertices and 153 edges. It has chromatic number 3, chromatic index 3, radius 7, diameter 7 and girth 9. I
McGee graph
In the mathematical field of graph theory, the McGee graph or the (3-7)-cage is a 3-regular graph with 24 vertices and 36 edges. The McGee graph is the unique (3,7)-cage (the smallest cubic graph of g
Bull graph
In the mathematical field of graph theory, the bull graph is a planar undirected graph with 5 vertices and 5 edges, in the form of a triangle with two disjoint pendant edges. It has chromatic number 3
Double-star snark
In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges. In 1975, Rufus Isaacs introduced two infinite families of snarks—the flower snark and the , a
Harries graph
In the mathematical field of graph theory, the Harries graph or Harries (3-10)-cage is a 3-regular, undirected graph with 70 vertices and 105 edges. The Harries graph has chromatic number 2, chromatic
110-vertex Iofinova-Ivanov graph
The 110-vertex Iofinova-Ivanov graph is, in graph theory, a semi-symmetric cubic graph with 110 vertices and 165 edges.
Balaban 10-cage
In the mathematical field of graph theory, the Balaban 10-cage or Balaban (3,10)-cage is a 3-regular graph with 70 vertices and 105 edges named after Alexandru T. Balaban. Published in 1972, It was th
Cameron graph
The Cameron graph is a strongly regular graph of parameters .
Ellingham–Horton graph
In the mathematical field of graph theory, the Ellingham–Horton graphs are two 3-regular graphs on 54 and 78 vertices: the Ellingham–Horton 54-graph and the Ellingham–Horton 78-graph. They are named a
Krackhardt kite graph
In graph theory, the Krackhardt kite graph is a simple graph with ten nodes. The graph is named after David Krackhardt, a researcher of social network theory. Krackhardt introduced the graph in 1990 t