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A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

The cubitruncated cuboctahedral graph is the skeleton of the cubitruncated cuboctahedron, which is the only uniform polyhedron for which this is the case. It is illustrated ...

The cuboctahedron, also called the heptaparallelohedron or dymaxion (the latter according to Buckminster Fuller; Rawles 1997), is the Archimedean solid with faces 8{3}+6{4}. ...

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first ...

The Danzer graph is the Levi graph of the Danzer configuration (Boben et al. 2015). It has 70 vertices and 140 edges and is quartic, bipartite, self-dual, and unit-distance. ...

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 ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...