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The moth graph is the 6-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["MothGraph"].

A graph with projective plane crossing number equal to 0 may be said to be projective planar. Examples of projective planar graphs with graph crossing number >=2 include the ...

A Laman graph is a graph satisfying Laman's theorem. In other words, it is a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G and for which ...

The A graph is the graph on 6 vertices illustrated above. Unfortunately, at least one author (Farrugia 1999, p. 2) uses the term "A-graph" to refer to the 5-node bull graph. ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...

A connected graph is said to be highly irregular if the neighbors of each vertex have distinct vertex degrees. Highly irregular graphs exist on all orders except 3, 5 and 7, ...

The Weisfeiler-Leman dimension dim_(WL)(G) of a graph G, sometimes known as the WL dimension, is the smallest integer d such that the d-dimensional Weisfeiler-Leman algorithm ...

The Lemke graph is the 8-node graph with 13 edges illustrated above (Lemke and Kleitman 1989, Hurlbert 2011, Hurlbert 2013). The Lemke graph is the smallest graph that does ...

A sextic graph is a regular graph of degree six. The numbers of simple sextic graphs on n=7, 8, ... nodes are 1, 1, 4, 21, 266, 7846, 367860, ... (OEIS A006822). Examples are ...

An empty graph on n nodes consists of n isolated nodes with no edges. Such graphs are sometimes also called edgeless graphs or null graphs (though the term "null graph" is ...