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A graph is k-edge-connected if there does not exist a set of k-1 edges whose removal disconnects the graph (Skiena 1990, p. 177). The maximum edge connectivity of a given ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

The thickness (or depth) t(G) (Skiena 1990, p. 251; Beineke 1997) or theta(G) (Harary 1994, p. 120) of a graph G is the minimum number of planar edge-induced subgraphs P_i of ...

A Mersenne number is a number of the form M_n=2^n-1, (1) where n is an integer. The Mersenne numbers consist of all 1s in base-2, and are therefore binary repunits. The first ...

A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely ...

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

A regular graph that is edge-transitive but not vertex-transitive is called a semisymmetric graph (Marušič and Potočnik 2001). In contrast, any graph that is both ...

A Wieferich prime is a prime p which is a solution to the congruence equation 2^(p-1)=1 (mod p^2). (1) Note the similarity of this expression to the special case of Fermat's ...