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Let v(G) be the number of vertices in a graph G and h(G) the length of the maximum cycle in G. Then the shortness exponent of a class of graphs G is defined by sigma(G)=lim ...

Let S be a set of simple polygonal obstacles in the plane, then the nodes of the visibility graph of S are just the vertices of S, and there is an edge (called a visibility ...

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

The great rhombicosidodecahedral graph is the Archimedean graph on 120 vertices and 180 edges that is the skeleton of the great rhombicosidodecahedron as well as the uniform ...

Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as ...

There are a number of graphs associated with T. I. (and C. T.) Zamfirescu. The Zamfirescu graphs on 36 and 75 vertices, the former of which is a snark, appear in Zamfirescu ...

A diagonal matrix D=diag(d_1,...,d_n) sometimes also called the valency matrix corresponding to a graph that has the vertex degree of d_i in the ith position (Skiena 1990, p. ...

An edge-induced subgraph is a subset of the edges of a graph G together with any vertices that are their endpoints. The subgraph induced by a set of edges can be computed in ...

Suppose that G is a pseudograph, E is the edge set of G, and C is the family of edge sets of graph cycles of G. Then C obeys the axioms for the circuits of a matroid, and ...

A two-graph (V,Delta) on nodes V is a collection Delta of unordered triples of the vertices (the so-called "odd triples") such that each 4-tuple of V contains an even number ...