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A graph G is a hypotraceable graph if G has no Hamiltonian path (i.e., it is not a traceable graph), but G-v has a Hamiltonian path (i.e., is a traceable graph) for every v ...

A graph G on more than two vertices is said to be k-connected (or k-vertex connected, or k-point connected) if there does not exist a vertex cut of size k-1 whose removal ...

The composition G=G_1[G_2] of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with point vertex V_1×V_2 and u=(u_1,u_2) ...

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 ...

The tetragonal antiwedge graph is the skeleton of the tetragonal antiwedge. It is a has 6 vertices, 10 edges, and 6 faces. The tetragonal antiwedge graph is self-dual and is ...

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 ...

A Meyniel graph, also called a very strongly perfect graph, is a graph in which every odd cycle of length five or more has at least two chords. Meyniel graphs are perfect. ...

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. ...

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