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The McLaughlin graph is a 112-regular graph on 275 nodes and 15400 edges that can be constructed from the Witt design. It is distance-regular with intersection array ...

The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...

The set of all zero-systems of a group G is denoted B(G) and is called the block monoid of G since it forms a commutative monoid under the operation of zero-system addition ...

Based on a problem in particle physics, Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) is the multinomial ...

A Lie algebra over an algebraically closed field is called exceptional if it is constructed from one of the root systems E_6, E_7, E_8, F_4, and G_2 by the Chevalley ...

The eccentricity epsilon(v) of a graph vertex v in a connected graph G is the maximum graph distance between v and any other vertex u of G. For a disconnected graph, all ...

Let G(V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t(n,k)<=((k-1)n^2)/(2k), where t(n,k) is the edge count. (Note ...

First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge e of Z^d is assigned a nonnegative random variable ...

The Golay code is a perfect linear error-correcting code. There are two essentially distinct versions of the Golay code: a binary version and a ternary version. The binary ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...