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The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs. The Goldner-Harary graph (Goldner and Harary 1975a, ...

A graph G=(V,E) is an interval graph if it captures the intersection relation for some set of intervals on the real line. Formally, P is an interval graph provided that one ...

A transposition graph G_n is a graph whose nodes correspond to permutations and edges to permutations that differ by exactly one transposition (Skiena 1990, p. 9, Clark ...

A unicyclic graph is a connected graph containing exactly one cycle (Harary 1994, p. 41). A connected unicyclic graph is therefore a pseudotree that is not a tree. ...

The M_(22) graph, also known as the 77-graph, is a strongly regular graph on 77 nodes related to the Mathieu group M_(22) and to the Witt design. It is illustrated above in ...

The small rhombicuboctahedral graph is a quartic graph on 24 nodes and 48 edges that corresponds to the skeleton of the small rhombicuboctahedron. It has graph diameter 5, ...

The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...

A nonhamiltonian graph is a graph that is not Hamiltonian. All disconnected graphs are therefore nonhamiltoinian, as are acylic graphs. Classes of connected graphs that are ...

A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

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 ...