field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v...

strongly regular graph is a distance-regular graph with diameter 2 whenever μ is non-zero. It is a locally linear graph whenever λ = 1. A strongly regular graph...

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular...

mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two...

In graph theory, a walk-regular graph is a simple graph where the number of closed walks of any length ℓ {\displaystyle \ell } from a vertex to itself...

Biggs–Smith graph. The ten distance-transitive graphs listed above, together with the Foster graph and the Biggs–Smith graph, are the only cubic distance-transitive...

distinct distance-regular graph; the intersection array of J ( 8 , 2 ) {\displaystyle J(8,2)} is shared with three other distance-regular graphs that are...

complete graphs that may be of varying sizes. Unlike the Hamming graphs H(d,q), the graphs in this more general class are not necessarily distance-regular, but...

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...

of graphs based on symmetry (such as symmetric graphs, vertex-transitive graphs, edge-transitive graphs, distance-transitive graphs, distance-regular graphs...

regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph). Finite vertex-transitive graphs include the symmetric graphs...

In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting...

Petersen graph can be transformed into every other such path by a symmetry of the graph. It is one of only 13 cubic distance-regular graphs. The automorphism...

It is a distance-transitive graph (see the Foster census) and therefore distance regular. There are 24 perfect matchings in the Heawood graph; for each...

Bruijn graph Dense graph Dipole graph Directed acyclic graph Directed graph Distance regular graph Distance-transitive graph Edge-transitive graph Interval...

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...

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...

mathematical field of graph theory, the Shrikhande graph is a graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices...

arc-transitive, and distance-transitive graphs; strongly regular graphs and their generalizations distance-regular graphs. Two edges of a graph are called adjacent...

In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if...

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...

In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space ⁠ R n {\displaystyle \mathbb {R}...

demihypercube, formed by connecting pairs of vertices at distance exactly two from each other in the hypercube graph. That is, it is the half-square of the hypercube...

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...

folded cube graphs provide a class of triangle-free graphs with chromatic number four and arbitrarily large odd girth. As a distance-regular graph with odd...

Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Qn has 2n vertices, 2n − 1n edges, and is a regular graph with n edges...

goes to 1. A pair of regular graphs are cospectral if and only if their complements are cospectral. A pair of distance-regular graphs are cospectral if and...

In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of...

studying strongly regular graphs and two-graphs. The distance matrix has in position (i, j) the distance between vertices vi and vj. The distance is the length...

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...