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A triangle-replaced graph T(G) is a cubic graph in which each vertex is replaced by a triangle graph such that each vertex of the triangle is connected to one of the ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

A loop of an graph is degenerate edge that joins a vertex to itself, also called a self-loop. A simple graph cannot contain any loops, but a pseudograph can contain both ...

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

Two points on a surface which are opposite to each other but not farthest from each other (e.g., the midpoints of opposite edges of a cube) are said to be transitive points. ...

The Hall graph is a distance-transitive graph on 65 vertices having intersection array {10,6,4,1;1,2,5} (Hall 1980). It is denoted Gamma^((3)) by Hall (1980) and was ...

The hexacode graph is the incidence graph of the unique symmetric transversal design STD_2[6;3]. It is also a bipartite (0,2)-graph. The hexacode graph is a ...

A group is called k-transitive group if there exists a set of elements on which the group acts faithfully and k-transitively. It should be noted that transitivity computed ...

The Delsarte graph is a strongly regular graph on 243 vertices with regular parameters (nu,k,lambda,mu)=(243,110,37,60). It is distance-regular as well as distance-transitive ...