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Let (P,B) denote a configuration with v points P={p_1,...,p_v} and b lines ("blocks") B=(B_1,...,B_b). Then the Levi graph L(P,B), also called the incidence graph, of a ...

A septic graph is a regular graph of degree seven. The numbers of (not necessarily connected) simple septic graphs on n=8, 10, 12, ... vertices are 1, 5, 1547, 21609301, ...

The Clebsch graph, also known as the Greenwood-Gleason graph (Read and Wilson, 1998, p. 284) and illustrated above in a number of embeddings, is a strongly regular quintic ...

Let Y_n denote the graph with vertex set V(X_n), where X_n is the n-hypercube and two vertices are adjacent in Y_n iff they are at distance 1<=d<=2 in X_n. Y_n is not ...

The genus gamma(G) of a graph G is the minimum number of handles that must be added to the plane to embed the graph without any crossings. A graph with genus 0 is embeddable ...

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 ...

The Pell graph Pi_n is the graph defined as follows. Consider n-tuples of (0,1,2) such that maximal blocks of an odd number of 2's are forbidden. Take these as the vertices ...

Define an antipode of a given graph vertex v_i as a vertex v_j at greatest possible graph distance from v_i. Then an antipodal graph is a connected graph in which each vertex ...

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 ...

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...