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Heule graphs are a set of unit-distance graphs with chromatic number five derived by Marijn Heule in April 2018 to July 2918 from the 1581-vertex de Grey Graph (Heule 2018). ...

A holyhedron is polyhedron whose faces and holes are all finite-sided polygons and that contains at least one hole whose boundary shares no point with a face boundary. D. ...

As proposed by Hosoya (1971), the Hosoya index (also called Z-index) of a graph is defined by Z = sum_(k=0)^(n)|a_k| (1) = sum_(k=0)^(n)b_k, (2) where n is the number of ...

A lossless data compression algorithm which uses a small number of bits to encode common characters. Huffman coding approximates the probability for each character as a power ...

The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map. The identity function is ...

Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. The figure above shows independent sets ...

A product involving an infinite number of terms. Such products can converge. In fact, for positive a_n, the product product_(n=1)^(infty)a_n converges to a nonzero number iff ...

The number of different triangles which have integer side lengths and perimeter n is T(n) = P(n,3)-sum_(1<=j<=|_n/2_|)P(j,2) (1) = [(n^2)/(12)]-|_n/4_||_(n+2)/4_| (2) = ...

Divide a set of data into two groups (high and low) of equal size at the statistical median if there is an even number of data points, or two groups consisting of points on ...