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The Schläfli graph is a strongly regular graph on 27 nodes which is the graph complement of the generalized quadrangle GQ(2,4). It is the unique strongly regular graph with ...

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 ...

"The" tetrahedral graph is the Platonic graph that is the unique polyhedral graph on four nodes which is also the complete graph K_4 and therefore also the wheel graph W_4. ...

An m-gonal n-cone graph, also called the n-point suspension of C_m or generalized wheel graph (Buckley and Harary 1988), is defined by the graph join C_m+K^__n, where C_m is ...

The "contiguous USA graph" is the graph whose vertices represent the contiguous 48 states of the United States plus the District of Columbia (DC) and whose edges connect ...

The diamond graph is the simple graph on 4 nodes and 5 edges illustrated above (Brandstädt et al. 1987, p. 18). It is isomorphic to the complete tripartite graph K_(1,1,2) ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 and m=2,3, but only a small ...

The helm graph H_n is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle. Helm graphs are graceful (Gallian 2018), with the odd ...

The m×n king graph is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a king. The number ...