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Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

The detour polynomial of a graph G is the characteristic polynomial of the detour matrix of G. Precomputed detour polynomials for many named graphs are available in the ...

A cograph (or "complement-reducible graph") is simple graph defined by the criteria 1. K_1 is a cograph, 2. If X is a cograph, then so is its graph complement, and 3. If X ...

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

A bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board). To form the ...

Petersen's theorem states that every cubic graph with no bridges has a perfect matching (Petersen 1891; Frink 1926; König 1936; Skiena 1990, p. 244). In fact, this theorem ...

The tetragonal antiwedge graph is the skeleton of the tetragonal antiwedge. It is a has 6 vertices, 10 edges, and 6 faces. The tetragonal antiwedge graph is self-dual and is ...

The mean distance of a (connected) graph is the mean of the elements of its graph distance matrix. Closed forms for some classes of named graphs are given in the following ...

Call a graph vertex m(a,b,c) a median of a graph G if it lies on all shortest paths between each pair of vertices (a,b), (b,a), and (c,a) in G. A median graph is then defined ...

An edge-transitive graph is a graph such that any two edges are equivalent under some element of its automorphism group. More precisely, a graph is edge-transitive if for all ...