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The gem graph is the fan graph F_(4,1) illustrated above. It is implemented in the Wolfram Language as GraphData["GemGraph"].

The Pappus graph is a cubic symmetric distance-regular graph on 18 vertices, illustrated above in three embeddings. It is Hamiltonian and can be represented in LCF notation ...

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 ...

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 n-ladder graph can be defined as L_n=P_2 square P_n, where P_n is a path graph (Hosoya and Harary 1993; Noy and Ribó 2004, Fig. 1). It is therefore equivalent to the 2×n ...

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 Petersen graph is the cubic graph on 10 vertices and 15 edges which is the unique (3,5)-cage graph (Harary 1994, p. 175), as well as the unique (3,5)-Moore graph. It can ...

The Nauru graph is the name given by Eppstein (2007) to the generalized Petersen graph GP(12,5) on 24 nodes and 36 edges which is also cubic symmetric graph F_(024)A, the ...

A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph K_5, and the unique quartic graph on six nodes is the octahedral ...