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The Georges graph, illustrated above, is 50-node graph which is the smallest currently known example of a 3-connected bicubic nonhamiltonian graph. It is implemented in the ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (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 Golomb graph is a unit-distance graph discovered around 1960-1965 by Golomb (Soifer 2008, p. 19). It is implemented in the Wolfram Language as GraphData["GolombGraph"]. A ...

The triangular snake graph TS_n is the graph on n vertices with n odd defined by starting with the path graph P_(n-1) and adding edges (2i-1,2i+1) for i=1, ..., n-1. The ...

The tetragonal antiwedge graph is the skeleton of the tetragonal antiwedge. It is a has 6 vertices, 10 edges, and 6 faces. The tetragonal antiwedge graph is self-dual and is ...

Cubic symmetric graphs are sometimes called Foster graphs and denoted F_(nnn)X, where nnn is the vertex count and X is a letter A, B, C, ... indicating the particular such ...

The deltoidal icositetrahedral graph is Archimedean dual graph which is the skeleton of the deltoidal icositetrahedron. It is implemented in the Wolfram Language as ...

The cubic Archimedean graph on 24 nodes and 36 edges that is the skeleton of the truncated cube. It is implemented in the Wolfram Language as ...

The pentagonal wedge graph is the skeleton of the pentagonal wedge. It is a has 8 vertices, 12 edges, and 6 faces. The pentagonal wedge graph is implemented in the Wolfram ...