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Tietze's graph is the cubic graph on 12 nodes and 18 edges illustrated above in a number of embeddings. It is implemented in the Wolfram Language as GraphData["TietzeGraph"]. ...

The Wormald graph is a unit-distance 4-chromatic graph with girth 5 on 13+5(13; 5)=6448 vertices.

There are several different definitions of the barbell graph. Most commonly and in this work, the n-barbell graph is the simple graph obtained by connecting two copies of a ...

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 ...

In general, an extremal graph is the largest graph of order n which does not contain a given graph G as a subgraph (Skiena 1990, p. 143). Turán studied extremal graphs that ...

The Pasch configuration is the unbalanced (6_2,4_3) configuration (since there are two lines through each of six points and three points on each of four lines) illustrated ...

The twinplex graph is the graph illustrated above in a number of embeddings which corresponds to the graph labeled Gamma_2 in Fischer and Little (2011). It is a cubic ...

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 ...

A distance graph with distance set (0,1].

The n-wheel complement graph W^__n is the graph complement of the n-wheel graph. For n>4, W^__n is isomorphic to the graph disjoint union of a circulant graph ...