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A nonplanar graph G is said to be critical nonplanar if the removal of a vertex results in a planar graph for every vertex of G. Critical nonplanar graphs differ from apex ...

A quartic nonhamiltonian graph is a quartic graph that is nonhamiltonian. A number of such graphs are illustrated above. Van Cleemput and Zamfirescu (2018) gave a 39-vertex ...

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 ...

Consider a star graph S_(n+1) consisting of a central hub vertex and n spokes, but instead of placing a single point at the end of each spoke, place k points along it (in ...

The cyclotomic graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a cube in the finite field GF(q). This graph is ...

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...

The tetrakis hexahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...

The Biggs-Smith graph is cubic symmetric graph F_(102)A on 102 vertices and 153 edges that is also distance-regular with intersection array {3,2,2,2,1,1,1;1,1,1,1,1,1,3} and ...