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The theorem, originally conjectured by Berge (1960, 1961), that a graph is perfect iff neither the graph nor its graph complement contains an odd graph cycle of length at ...

A 3-coloring of graph edges so that no two edges of the same color meet at a graph vertex (Ball and Coxeter 1987, pp. 265-266).

A Taylor graph is a distance-regular graph with intersection array {k,mu,1;1,mu,k}. A Taylor graph with these parameters has 2(k+1) vertices. The crown graphs K_2 square ...

The toroidal crossing number cr_(1)(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, ...

A graph is said to be unswitchable if it cannot be reduced to another graph with the same degree sequence by edge-switching. Conversely, a graph that can be reduced to ...

Wagner's theorem states that a graph is planar iff it does not contain K_5 or K_(3,3) as a graph minor.

The Wormald graph is a unit-distance 4-chromatic graph with girth 5 on 13+5(13; 5)=6448 vertices.

The Van Lint-Schrijver Graph graph is a weakly regular Hamiltonian graph on 162 vertices with parameters (nu,k,lambda,mu)=(162,(6),(0),(0,1)). It is distance-regular with ...

The cosecant cscz is the function defined by cscz = 1/(sinz) (1) = (2i)/(e^(iz)-e^(-iz)), (2) where sinz is the sine. The cosecant is implemented in the Wolfram Language as ...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...