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A fan graph F_(m,n) is defined as the graph join K^__m+P_n, where K^__m is the empty graph on m nodes and P_n is the path graph on n nodes. The case m=1 corresponds to the ...

The great dirhombicosidodecahedral graph is the skeleton of the great dirhombicosidodecahedron and the second octahedron 20-compound. It is illustrated above in a few ...

The triangular graph T_n=L(K_n) is the line graph of the complete graph K_n (Brualdi and Ryser 1991, p. 152). The vertices of T_n may be identified with the 2-subsets of ...

The folded n-cube graph, perhaps better termed "folded hypercube graph," is a graph obtained by merging vertices of the n-hypercube graph Q_n that are antipodal, i.e., lie at ...

The kite graph is the 5-vertex graph illustrated above (Brandstädt et al. 1987, p. 18). It is implemented in the Wolfram Language as GraphData["KiteGraph"]. Unfortunately, ...

A generalized hexagon is a generalized polygon of order 6. GH(1,2) is more commonly known as the Heawood graph, but is also the (3,6)-cage graph, the cubic vertex-transitive ...

The truncated pentakis dodecahedral graph, illustrated above in a pair of embeddings, is the skeleton of the truncated pentakis dodecahedron. It has 180 vertices, 270 edges, ...

The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes (20) (Skiena 1990, p. 186). It is implemented in the Wolfram Language as ...

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 Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...