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The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

A labeled graph G=(V,E) is a finite series of graph vertices V with a set of graph edges E of 2-subsets of V. Given a graph vertex set V_n={1,2,...,n}, the number of ...

Let a tree S be a subgraph of a cubic graph G. The graph excision G circleminus S is the graph resulting from removing the tree, then merging the edges. For example, if in ...

The term "null graph" is used both to refer to any empty graph and to the empty graph on 0 nodes. Because of the conflicting usage, it is probably best to avoid use of the ...

There are several differing definitions of the sun graph. ISGCI defines a (complete) n-sun graph as a graph on 2n nodes (sometimes also known as a trampoline graph; ...

The Poussin graph is the 15-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

A graph is said to be unswitchable if it cannot be reduced to another graph with the same degree sequence by edge-switching. Conversely, a graph that can be reduced to ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

A bridgeless graph, also called an isthmus-free graph, is a graph that contains no graph bridges. Examples of bridgeless graphs include complete graphs on n>2 nodes, cycle ...

A graph is said to be H^*-connected if it is either Hamilton-connected or Hamilton-laceable. S. Wagon (pers. comm., May. 20, 2013; Dupuis and Wagon 2014) conjecture that all ...