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Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 and m=2,3, but only a small ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

The degree of a graph vertex of a graph is the number of graph edges which touch the graph vertex, also called the local degree. The graph vertex degree of a point A in a ...

A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.

Vince and Bóna (2012) define an assembly tree T for a connected simple graph G on n nodes as a binary rooted tree with n leavesTree Leaf and n-1 internal nodes and satisfying ...

Bit rate (i.e., bits per second, abbreviated bps) is a measure of the number of data bits (digital 0s and 1s) transmitted each second in a digital communications channel. If ...

Given a sequence {a_i}_(i=1)^N, an n-moving average is a new sequence {s_i}_(i=1)^(N-n+1) defined from the a_i by taking the arithmetic mean of subsequences of n terms, ...

The bootstrap method is a computer-based method for assigning measures of accuracy to sample estimates (Efron and Tibshirani 1994). This technique allows estimation of the ...

According to Pólya, the Cartesian pattern is the resolution method for arithmetical or geometrical problems based on equations. The first step is to translate the question ...