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...

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...

is a Coxeter matrix. The Coxeter matrix can be conveniently encoded by a Coxeter diagram, as per the following rules. The vertices of the graph are labelled...

the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm. Coxeter was...

a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group...

Petersen graph. Only five connected vertex-transitive graphs with no Hamiltonian cycles are known: the complete graph K2, the Petersen graph, the Coxeter graph...

"From the Coxeter graph to the Klein graph", Journal of Graph Theory, 70: 1–9, arXiv:1002.1960, doi:10.1002/jgt.20597, S2CID 754481. Coxeter (1950), "Self-dual...

the Desargues graph, the Nauru graph, the Coxeter graph, the Tutte–Coxeter graph, the Dyck graph, the Foster graph and the Biggs–Smith graph. W. T. Tutte...

graph Coxeter graph Tutte–Coxeter graph Dyck graph Klein graph Foster graph Biggs–Smith graph The Rado graph Folkman graph Gray graph Ljubljana graph Tutte...

graphs include the Nauru graph and the McGee graph or (3,7)-cage graph, with 24 vertices. The smallest 11-crossing cubic graphs include the Coxeter graph...

{\displaystyle {\tilde {A}}_{n}} affine Coxeter group symmetry. It is represented by a Coxeter-Dynkin diagram as a cyclic graph of n + 1 nodes with one node ringed...

girth of 7 The Tutte–Coxeter graph (Tutte eight cage) has a girth of 8 For any positive integers g and χ, there exists a graph with girth at least g...

making it a square pyramidal number. The number of vertices in the Tutte–Coxeter graph. The measure of the central angle and exterior angle of a dodecagon...

In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of...

Klein graph, referenced as F056B, is the only cubic symmetric graph on 56 vertices which is not bipartite. It can be derived from the 28-vertex Coxeter graph...

question is the Coxeter plane of the symmetry group of the polygon, and the number of sides, h, is the Coxeter number of the Coxeter group. These polygons...

Singleton graph also contains the odd graph O(4), the Coxeter graph, and the Tutte-Coxeter graph as subgraphs. Take any edge of the Hoffman-Singleton graph, and...

Tetrahedral graph), K3,3, the Petersen graph, the Cubical graph, the Heawood graph, the Pappus graph, the Coxeter graph, the Tutte–Coxeter graph, the Dodecahedral...

In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first...

ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube was discovered in...

he helped popularize H.S.M. Coxeter's work, introducing terms such as Coxeter number, Coxeter group, and Coxeter graph. Tits died on 5 December 2021...

blank in the upper right, corresponding to directed graphs with underlying undirected graph any Coxeter diagram (of a finite group), can be defined formally...

the complete bipartite graphs Kn,n with girth four, the Heawood graph with degree 3 and girth 6, and the Tutte–Coxeter graph with degree 3 and girth...

{A}}_{n}} affine Coxeter group. It is given a Schläfli symbol t0,1{3[n+1]}, and is represented by a Coxeter-Dynkin diagram as a cyclic graph of n+1 nodes...

Goldberg–Coxeter construction or Goldberg–Coxeter operation (GC construction or GC operation) is a graph operation defined on regular polyhedral graphs with...

In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the...

as a graph, is Hamiltonian The Cayley graph of a finite Coxeter group is Hamiltonian (For more information on Hamiltonian paths in Cayley graphs, see...

complete graph K 2 {\displaystyle K_{2}} , the Petersen graph, the Coxeter graph and two graphs derived from the Petersen and Coxeter graphs by replacing...

Octahedral molecular geometry Octahedral symmetry Octahedral graph Octahedral sphere (Coxeter 1973) uses the greek letter 𝝓 (phi) to represent one of the...

Ljubljana graph on 112 vertices is the Levi graph of the Ljubljana configuration. Grünbaum, Branko (2006), "Configurations of points and lines", The Coxeter Legacy...