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Given a commutative unit ring R, and an R-module M, a sequence {x_1,...,x_n} of elements of R is called a regular sequence for M (or an M-sequence for short), if, for all ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. This partitions graphs into ...

The Weierstrass constant is defined as the value sigma(1|1,i)/2, where sigma(z|omega_1,omega_2) is the Weierstrass sigma function with half-periods omega_1 and omega_2. ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

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. Given a vertex cover of a graph, all ...

The metric dimension beta(G) (Tillquist et al. 2021) or dim(G) (Tomescu and Javid 2007, Ali et al. 2016) of a graph G is the smallest number of nodes required to identify all ...

T-integration, which stands for "tunable numerical integration," is a fast, accurate, and numerically stable numerical integration formula given by ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

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 ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...