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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 genus gamma(G) of a graph G is the minimum number of handles that must be added to the plane to embed the graph without any crossings. A graph with genus 0 is embeddable ...

The Harary index of a graph G on n vertices was defined by Plavšić et al. (1993) as H(G)=1/2sum_(i=1)^nsum_(j=1)^n(RD)_(ij), (1) where (RD)_(ij)={D_(ij)^(-1) if i!=j; 0 if ...

The Hermite polynomials H_n(x) are set of orthogonal polynomials over the domain (-infty,infty) with weighting function e^(-x^2), illustrated above for n=1, 2, 3, and 4. ...

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 graph G is hypohamiltonian if G is nonhamiltonian, but G-v is Hamiltonian for every v in V (Bondy and Murty 1976, p. 61). The Petersen graph, which has ten nodes, is the ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...