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A cubic nonplanar graph is a graph that is both cubic and nonplanar. The following table summarizes some named nonplanar cubic graphs. graph G |V(G)| utility graph 6 Petersen ...

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 ...

The hemiobelisk graph is the skeleton of the hemiobelisk. It has 7 vertices, 11 edges, and 6 faces. It is a minimal unit-distance forbidden graph. It is implemented in the ...

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 ...

The Egawa graph with parameters (p,s) is a distance-regular but not distance-transitive graph on 16^p4^s nodes. These graphs generalize the Doob graphs and give (s,4)-Hamming ...

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 ...

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 ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...