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A graph G is Hamilton-connected if every two vertices of G are connected by a Hamiltonian path (Bondy and Murty 1976, p. 61). In other words, a graph is Hamilton-connected if ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

The cube of a graph is defined as its third graph power.

The cubitruncated cuboctahedral graph is the skeleton of the cubitruncated cuboctahedron, which is the only uniform polyhedron for which this is the case. It is illustrated ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...

An Eulerian graph is a graph containing an Eulerian cycle. The numbers of Eulerian graphs with n=1, 2, ... nodes are 1, 1, 2, 3, 7, 15, 52, 236, ... (OEIS A133736), the first ...

A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with degree at most 2. The numbers of spiders on n=1, 2, ... ...

The Berlekamp-van Lint-Seidel graph is the Hamiltonian strongly regular graph on 243 vertices with parameters (243,22,1,2). It is also distance-regular with intersection ...

The truncated dodecadodecahedral graph is the skeleton of the truncated dodecadodecahedron, which is the only uniform polyhedron for which this is the case. It will be ...

A Berge graph is a simple graph that contains no odd graph hole and no odd graph antihole. The strong perfect graph theorem asserts that a graph is perfect iff it is a Berge ...