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Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...

A simple continued fraction is a special case of a generalized continued fraction for which the partial numerators are equal to unity, i.e., a_n=1 for all n=1, 2, .... A ...

There appears to be no term in standard use for a graph with graph crossing number 1. Furthermore, the terms "almost planar" and "1-planar" are used in the literature for ...

The Sombor energy of a graph is defined as the graph energy of its Sombor matrix, i.e., the sum of the absolute values of the eigenvalues of its Sombor matrix.

The Sombor index of a graph is defined as half the sum of the matrix elements of its Sombor matrix.

The Sombor matrix A_(Sombor) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the graph. In ...

The Sombor spectral radius rho_(Sombor) of a graph is defined as the largest eigenvalue of the Sombor matrix. Liu et al. (2022) shows that for any tree, ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...