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Knuth (2008, p. 44) terms the 24-vertex graph based on the notes of the musical scale illustrated above the "musical graph." This graph can be seen to be the 24-vertex case ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...

The gear graph, also sometimes known as a bipartite wheel graph (Brandstädt et al. 1987), is a wheel graph with a graph vertex added between each pair of adjacent graph ...

A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is ...

A set of numbers a_0, a_1, ..., a_(m-1) (mod m) form a complete set of residues, also called a covering system, if they satisfy a_i=i (mod m) for i=0, 1, ..., m-1. For ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be geometric if ac=b^2. In particular, such a triple is geometric if its terms form a geometric sequence ...

The circumference of a graph is the length of any longest cycle in a graph. Hamiltonian graphs on n>1 vertices therefore have circumference of n. For a cyclic graph, the ...

Hackenbush is a game in combinatorial game theory in which player Left can delete any bLue edge, player Right can delete any Red edge, and either player can delete Green ...

For a real number x in (0,1), let m be the number of terms in the convergent to a regular continued fraction that are required to represent n decimal places of x. Then for ...

A weakly perfect graph is a graph for which omega(G)=chi(G) (without any requirement that this condition also hold on induced subgraphs, which is required for a graph to be ...