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The Royle graphs are the two unique simple graphs on eight nodes whose sigma polynomials have nonreal roots (Read and Wilson 1998, p. 265). The sigma polynomials of these ...

The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and ...

The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs. The Goldner-Harary graph (Goldner and Harary 1975a, ...

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 ...

The skeleton of the tesseract, commonly denoted Q_4, is a quartic symmetric graph with girth 4 and diameter 4. The automorphism group of the tesseract is of order 2^7·3=384 ...

Random walk trajectories which are composed of self-similar jumps. They are described by the Lévy distribution.

The Fritsch graph is the 9-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 Gray graph is a cubic semisymmetric graph on 54 vertices. It was discovered by Marion C. Gray in 1932, and was first published by Bouwer (1968). Malnič et al. (2002) ...

The Soifer graph, illustrated above in a number of embeddings, is a planar graph on 9 nodes that tangles the Kempe chains in Kempe's algorithm and thus provides an example of ...

The truncated Witt graph is the graph on 506 vertices related to a 4-(23,8,4) design (Brouwer et al. 1989, p. 367). It is called the M_(23) graph by van Dam and Haemers ...