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Given a ring R with identity, the general linear group GL_n(R) is the group of n×n invertible matrices with elements in R. The general linear group GL_n(q) is the set of n×n ...

The girth of a graphs is the length of one of its (if any) shortest graph cycles. Acyclic graphs are considered to have infinite girth (Skiena 1990, p. 191). The girth of a ...

The complement of a graph G, sometimes called the edge-complement (Gross and Yellen 2006, p. 86), is the graph G^', sometimes denoted G^_ or G^c (e.g., Clark and Entringer ...

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

The graph sum of graphs G and H is the graph with adjacency matrix given by the sum of adjacency matrices of G and H. A graph sum is defined when the orders of G and H are ...

The Grassmann graph J_q(n,k) is defined such that the vertices are the k-dimensional subspaces of an n-dimensional finite field of order q and edges correspond to pairs of ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

Given a distance-regular graph G with integers b_i,c_i,i=0,...,d such that for any two vertices x,y in G at distance i=d(x,y), there are exactly c_i neighbors of y in ...

A point process N on R is said to be interval stationary if for every r=1,2,3,... and for all integers i_i,...,i_r, the joint distribution of {tau_(i_1+k),...,tau_(i_r+k)} ...