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An extremal graph in which the forced triangles are all the same color. Call R the number of red monochromatic forced triangles and B the number of blue monochromatic forced ...

Given a set A, let N(A) be the set of neighbors of A. Then the bipartite graph G with bipartitions X and Y has a perfect matching iff |N(A)|>=|A| for all subsets A of X.

The hyperbolic secant is defined as sechz = 1/(coshz) (1) = 2/(e^z+e^(-z)), (2) where coshz is the hyperbolic cosine. It is implemented in the Wolfram Language as Sech[z]. On ...

A set in Euclidean space R^d is convex set if it contains all the line segments connecting any pair of its points. If the set does not contain all the line segments, it is ...

The Lorenz asymmetry coefficient is a summary statistic of the Lorenz curve that measures the degree of asymmetry of a Lorenz curve. The Lorenz asymmetry coefficient is ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...

A periodic minimal surface constructed by Schwarz using the following two principles: 1. If part of the boundary of a minimal surface is a straight line, then the reflection ...

An unduloid, also called an onduloid, is a surface of revolution with constant nonzero mean curvature. It is a roulette obtained from the path described by the foci of a ...

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...

Flower graphs are a name given in this work to the generalization of the flower snarks J_n for positive n=5, 7, 9, ... to all integer n>=5. They are illustrated above for n=5 ...