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The graph complement of a perfect graph is itself perfect. Originally known as the weak perfect graph conjecture (Fulkerson 1971), the result was subsequently proved by ...

A functional graph is a directed graph in which each vertex has outdegree one, and can therefore be specified by a function mapping {1,...,n} onto itself. Functional graphs ...

There are several different definitions of the barbell graph. Most commonly and in this work, the n-barbell graph is the simple graph obtained by connecting two copies of a ...

In general, an extremal graph is the largest graph of order n which does not contain a given graph G as a subgraph (Skiena 1990, p. 143). Turán studied extremal graphs that ...

The twinplex graph is the graph illustrated above in a number of embeddings which corresponds to the graph labeled Gamma_2 in Fischer and Little (2011). It is a cubic ...

The helm graph H_n is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle. Helm graphs are graceful (Gallian 2018), with the odd ...

The n-wheel complement graph W^__n is the graph complement of the n-wheel graph. For n>4, W^__n is isomorphic to the graph disjoint union of a circulant graph ...

A quartic symmetric graph is a symmetric graph that is also quartic (i.e., regular of degree 4). The numbers of symmetric quartic graphs on n=1, 2, ... are 0, 0, 0, 0, 1, 1, ...

The Harary graph H_(k,n) is a particular example of a k-connected graph with n graph vertices having the smallest possible number of edges. The smallest number of edges ...

A bicolorable graph G is a graph with chromatic number chi(G)<=2. A graph is bicolorable iff it has no odd graph cycles (König 1950, p. 170; Skiena 1990, p. 213; Harary 1994, ...