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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 ...

The Ljubljana graph is a graph on 112 vertices that is the third smallest cubic semisymmetric graph. It was discovered by Brouwer et al. (1993) and rediscovered by Conder et ...

A graph Gamma is locally Petersen if, for each point t of Gamma, the graph induced by Gamma on all points adjacent to t (i.e., the neighborhood graph) is isomorphic to the ...

The log-likelihood function F(theta) is defined to be the natural logarithm of the likelihood function L(theta). More precisely, F(theta)=lnL(theta), and so in particular, ...

Given n matches (i.e., rigid unit line segments), find the number of topologically distinct planar arrangements which can be made (Gardner 1991). In this problem, two matches ...