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A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P=(X,<=), where X is ...

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

A prism graph, denoted Y_n, D_n (Gallian 1987), or Pi_n (Hladnik et al. 2002), and sometimes also called a circular ladder graph and denoted CL_n (Gross and Yellen 1999, p. ...

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 molecular topological index is a graph index defined by MTI=sum_(i=1)^nE_i, where E_i are the components of the vector E=(A+D)d, with A the adjacency matrix, D the graph ...

Triskaidekaphobia is the fear of 13, a number commonly associated with bad luck in Western culture. While fear of the number 13 can be traced back to medieval times, the word ...

Elliptic curve primality proving, abbreviated ECPP, is class of algorithms that provide certificates of primality using sophisticated results from the theory of elliptic ...

Given a positive integer m>1, let its prime factorization be written m=p_1^(a_1)p_2^(a_2)p_3^(a_3)...p_k^(a_k). (1) Define the functions h(n) and H(n) by h(1)=1, H(1)=1, and ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...