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The (connected) caveman graph is a graph arising in social network theory formed by modifying a set of isolated k-cliques (or "caves") by removing one edge from each clique ...

The Hall-Janko graph, also known as the Hall-Janko-Wales graph, is a strongly regular graph on 100 nodes with parameters (nu,k,lambda,mu)=(100,36,14,12). It is also a ...

The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs, including the Herschel graph and the Goldner-Harary ...

The Meringer graph is one of the four (5,5)-cage graphs, discovered by Meringer (1999) after it had long been thought that only three such cages existed. Like the other ...

Erdős and Heilbronn (Erdős and Graham 1980) posed the problem of estimating from below the number of sums a+b where a in A and b in B range over given sets A,B subset= Z/pZ ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges lambda(G) whose deletion from a graph G disconnects G. In other words, it ...

Proper covers are defined as covers of a set X which do not contain the entire set X itself as a subset (Macula 1994). Of the five covers of {1,2}, namely {{1},{2}}, {{1,2}}, ...

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 ...

Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted ...