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An Ore graph is a graph that satisfies Ore's theorem, i.e., a graph G for which the sums of the degrees of nonadjacent vertices is greater than or equal to the number of ...

An antelope graph (Jelliss 2019) is a graph formed by all possible moves of a hypothetical chess piece called an "antelope" which moves analogously to a knight except that it ...

A graph G that becomes disconnected when removing a suitable complete subgraph K, called a vertex cut, is said to be quasiseparable. The two simplest cases are those where K ...

A self-complementary graph is a graph which is isomorphic to its graph complement. The numbers of simple self-complementary graphs on n=1, 2, ... nodes are 1, 0, 0, 1, 2, 0, ...

A Mongolian tent graph is defined as the graph obtained from the grid graph P_m square P_n for odd n by adding an extra vertex above the graph and joining every other vertex ...

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 ...

Several differing definitions of almost planar (as well as nearly planar) have been used in the literature (cf. Lipton et al. 2016). For example, Gubser (1996) defines an ...

A bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board). To form the ...

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 ...

A split graph is a graph whose vertices can be partitioned into a clique and an independent vertex set. Equivalently, it is a chordal graph whose graph complement is also ...