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A chordal graph is a simple graph in which every graph cycle of length four and greater has a cycle chord. In other words, a chordal graph is a graph possessing no chordless ...

A graph G is a hypotraceable graph if G has no Hamiltonian path (i.e., it is not a traceable graph), but G-v has a Hamiltonian path (i.e., is a traceable graph) for every v ...

The icosahedral graph is the Platonic graph whose nodes have the connectivity of the regular icosahedron, as well as the great dodecahedron, great icosahedron Jessen's ...

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...

The Frucht graph is smallest cubic identity graph (Skiena 1990, p. 185). It is implemented in the Wolfram Language as GraphData["FruchtGraph"]. It has 12 vertices and 18 ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

The McLaughlin graph is a 112-regular graph on 275 nodes and 15400 edges that can be constructed from the Witt design. It is distance-regular with intersection array ...

The middle layer graph of order n is the graph whose vertex set consists of all bitstrings of length 2n+1 that have exactly n or n+1 entries equal to 1, with an edge between ...

Every planar graph (i.e., graph with graph genus 0) has an embedding on a torus. In contrast, toroidal graphs are embeddable on the torus, but not in the plane, i.e., they ...