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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 ...

Das (2018) defines the triameter of a connected graph G with vertex set V and vertex count at least 3 as tr(G)=max{d(u,v)+d(v,w)+d(u,w):u,v,w in V}, where d(i,j) is the graph ...

The hexacode graph is the incidence graph of the unique symmetric transversal design STD_2[6;3]. It is also a bipartite (0,2)-graph. The hexacode graph is a ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

The pentakis icosidodecahedral graph, illustrated above, is a graph on 42 vertices that is the skeleton of the pentakis icosidodecahedron.

The Hajós graph (Brandstädt et al. 1987, Berge 1989) is another name for the Sierpiński sieve graph S_2, which is isomorphic to the 2-sun graph. However, the term is also ...

The parachute graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["ParachuteGraph"].

The parapluie (French for 'umbrella') graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["ParapluieGraph"].

The Grötzsch graph is smallest triangle-free graph with chromatic number four. It is identical to the Mycielski graph of order four, and is implemented as ...

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