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A noneulerian graph is a graph that is not Eulerian. The numbers of simple noneulerian graphs on n=1, 2, ... nodes are 2, 3, 10, 30, 148, 1007, 12162, 272886, ... (OEIS ...

A linklessly embeddable graph is a graph having the property that there exists an embedding in three dimensions that does not contain a nontrivial link. A graph is linklessly ...

The truncated Witt graph is the graph on 506 vertices related to a 4-(23,8,4) design (Brouwer et al. 1989, p. 367). It is called the M_(23) graph by van Dam and Haemers ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

The term "Euler graph" is sometimes used to denote a graph for which all vertices are of even degree (e.g., Seshu and Reed 1961). Note that this definition is different from ...

A zebra graph is a graph formed by all possible moves of a hypothetical chess piece called a "zebra" which moves analogously to a knight except that it is restricted to moves ...

A quintic nonhamiltonian graph is a quintic graph that is nonhamiltonian. A number of such graphs are illustrated above. Owens (1980) showed that there exists a ...

The Norton-Smith graph is a weakly regular graph on 1134 vertices with regular parameters (nu,k,lambda,mu)=(1134,117,36,(0,12)). It is distance-regular as well as ...

An edge-transitive graph is a graph such that any two edges are equivalent under some element of its automorphism group. More precisely, a graph is edge-transitive if for all ...

A two-graph (V,Delta) on nodes V is a collection Delta of unordered triples of the vertices (the so-called "odd triples") such that each 4-tuple of V contains an even number ...