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Given a set A, let N(A) be the set of neighbors of A. Then the bipartite graph G with bipartitions X and Y has a perfect matching iff |N(A)|>=|A| for all subsets A of X.

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

An independent dominating set of a graph G is a set of vertices in G that is both an independent vertex set and a dominating set of G. The minimum size of an independent ...

The sum I over all internal (circular) nodes of the paths from the root of an extended binary tree to each node. For example, in the tree above, the internal path length is ...

An intrinsically linked graph is a graph having the property that any embedding of it in three dimensions contains a nontrivial link. A graph is intrinsically linked iff it ...

Let i_k(G) be the number of irredundant sets of size k in a graph G, then the irredundance polynomial R_G(x) of G in the variable x is defined as ...

The Ivanov-Ivanov-Faradjev graph is a distance-regular graph on 990 vertices (Brouwer et al. 1989, p. 369). It has intersection array {7,6,4,4,4,1,1,1;1,1,1,2,4,4,6,7} and is ...

The Koolen-Riebeek graph is a weakly regular graph on 486 vertices with parameters (nu,k,lambda,mu)=(486,45,0,(0,9)). It is distance-regular but not distance-transitive with ...

A linklessly embeddable graph is a graph having the property that there exists an embedding in three dimensions that does not contain a nontrivial link. A graph is linklessly ...

The Livingstone graph is a distance-transitive graph on 266 vertices defined in terms of the Janko group J_1. It has intersection array {11,10,6,1;1,1,5,11}. The Livingstone ...