Search Results for ""

A number of strongly regular graphs of several types derived from combinatorial design were identified by Goethals and Seidel (1970). Theorem 2.4 of Goethals and Seidel ...

Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.

The cuboctahedral graph is an Archimedean quartic symmetric graph on 12 nodes and 24 edges that is the skeleton of the cuboctahedron, as well as the uniform ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

The Moser spindle is the 7-node unit-distance graph illustrated above (Read and Wilson 1998, p. 187). It is sometimes called the Hajós graph (e.g., Bondy and Murty 2008. p. ...

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 leg of a right triangle (i.e., a side adjacent the right angle) is also known as a cathetus (plural: catheti). While this usage is rather rare in English, the terms ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

In general, a graph product of two graphs G and H is a new graph whose vertex set is V(G)×V(H) and where, for any two vertices (g,h) and (g^',h^') in the product, the ...

The de Grey-Haugstrup graphs are two 6-chromatic graphs on 47 and 48 vertices that are unit-distance in 3 dimensions (de Grey and Haugstrup 2020).