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If two numbers b and c have the property that their difference b-c is integrally divisible by a number m (i.e., (b-c)/m is an integer), then b and c are said to be "congruent ...

The generalized Petersen graph GP(n,k), also denoted P(n,k) (Biggs 1993, p. 119; Pemmaraju and Skiena 2003, p. 215), for n>=3 and 1<=k<=|_(n-1)/2_| is a connected cubic graph ...

A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian. The ...

A biconnected graph is a connected graph having no articulation vertices (Skiena 1990, p. 175). An equivalent definition for graphs on more than two vertices is a graph G ...

Given two positive integers n and k, the bipartite Kneser graph H(n,k) is the graph whose two bipartite sets of vertices represent the k-subsets and (n-k)-subsets of ...

It is thought that the totient valence function N_phi(m)>=2, i.e., if there is an n such that phi(n)=m, then there are at least two solutions n. This assertion is called ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

A cubic vertex-transitive graph is a cubic graph that is vertex transitive. Read and Wilson (1998, pp. 161-163) enumerate all connected cubic vertex-transitive graphs on 34 ...

In continuum percolation theory, the so-called germ-grain model is an obvious generalization of both the Boolean and Boolean-Poisson models which is driven by an arbitrary ...