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A complete k-partite graph is a k-partite graph (i.e., a set of graph vertices decomposed into k disjoint sets such that no two graph vertices within the same set are ...

A square-free graph is a graph containing no graph cycles of length four. A simple graph is square-free iff c_4=1/8[Tr(A^4)-2m-2sum_(i!=j)a_(ij)^((2))]=0, where A is the ...

An antelope graph (Jelliss 2019) is a graph formed by all possible moves of a hypothetical chess piece called an "antelope" which moves analogously to a knight except that it ...

A cubic semisymmetric graph is a graph that is both cubic (i.e., regular of degree 3) and semisymmetric (i.e., edge- but not vertex-transitive). The four smallest cubic ...

A giraffe graph is a graph formed by all possible moves of a hypothetical chess piece called a "giraffe" which moves analogously to a knight except that it is restricted to ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

Define a = d(u,v)d(w,x) (1) b = d(u,w)d(v,x) (2) c = d(u,x)d(v,w), (3) where u, v, w, and x are vertices of a graph and d(i,j) is the graph distance between vertices i and j. ...

As defined in this work, a wheel graph W_n of order n, sometimes simply called an n-wheel (Harary 1994, p. 46; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 78), is a ...

The Golomb graph is a unit-distance graph discovered around 1960-1965 by Golomb (Soifer 2008, p. 19). It is implemented in the Wolfram Language as GraphData["GolombGraph"]. A ...

A Halin graph, sometimes known as a roofless polyhedron, is a polyhedral graph constructed from a planar embedding of a tree having four or more vertices, no vertices of ...