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The Perkel graph is a weakly regular graph on 57 vertices and 171 edges, shown above in several embeddings. It is the unique distance-regular graph with intersection array ...

One of the operations exists exists (called the existential quantifier) or for all forall (called the universal quantifier, or sometimes, the general quantifier). However, ...

As shown by Schur (1916), the Schur number S(n) satisfies S(n)<=R(n)-2 for n=1, 2, ..., where R(n) is a Ramsey number.

A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with degree at most 2. The numbers of spiders on n=1, 2, ... ...

Let h>=2 and let A_1, A_2, ..., A_h be sets of integers. The sumset A_1+A_2+...+A_h is the set of all integers of the form a_1+a_2+...+a_h, where a_i is a member of A_i for ...

"The" Sylvester graph is a quintic graph on 36 nodes and 90 edges that is the unique distance-regular graph with intersection array {5,4,2;1,1,4} (Brouwer et al. 1989, ...

A three-colorable graph G is a graph with chromatic number chi(G)<=3.

The triangular snake graph TS_n is the graph on n vertices with n odd defined by starting with the path graph P_(n-1) and adding edges (2i-1,2i+1) for i=1, ..., n-1. The ...

A group of three elements, also called a triad. A triple is therefore a 3-tuple.

The truncated great dodecahedral graph is the skeleton of the small stellated truncated dodecahedron and truncated great dodecahedron. It is illustrated above in a number of ...