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If the Tutte polynomial T(x,y) of a graph G is given by sumt_(rs)x^ry^s, then the matrix (t_(rs)) is called the rank matrix of G. For example, the Tutte matrix of the ...

A graph vertex in a graph is said to be an even node if its vertex degree is even.

Let G be a finite graph and v a vertex of G. The stabilizer of v, stab(v), is the set of group elements {g in Aut(G)|g(v)=v}, where Aut(g) is the graph automorphism group. ...

A self-avoiding polygon containing three corners of its minimal bounding rectangle. The anisotropic area and perimeter generating function G(x,y) and partial generating ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

A simple graph is a line graph of some simple graph iff if does not contain any of the above nine graphs, known in this work as Beineke graphs, as a forbidden induced ...

In combinatorial mathematics, the series-parallel networks problem asks for the number of networks that can be formed using a given number of edges. The edges can be ...

A two-coloring of a complete graph K_n of n nodes which contains exactly the number of monochromatic forced triangles and no more (i.e., a minimum of R+B where R and B are ...