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A sphere is defined as the set of all points in three-dimensional Euclidean space R^3 that are located at a distance r (the "radius") from a given point (the "center"). Twice ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3+a_2z^2+a_1z+a_0=0 (1) ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

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 quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...

The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers ...