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There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

The orthogonal decomposition of a matrix into lower trapezoidal matrices.

In determinant expansion by minors, the minimal number of transpositions of adjacent columns in a square matrix needed to turn the matrix representing a permutation of ...

A lobster graph, lobster tree, or simply "lobster," is a tree having the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007). The numbers of ...

A tripod is a tree having exactly three tree leaves (Pirnazar and Ullman 2002). The numbers of tripods on n=1, 2, ... vertices are 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, ...

Let ||A|| be the matrix norm associated with the matrix A and |x| be the vector norm associated with a vector x. Let the product Ax be defined, then ||A|| and |x| are said to ...

A diagonal of a square matrix which is traversed in the "northeast" direction. "The" skew diagonal (or "secondary diagonal") of an n×n square matrix is the skew diagonal from ...

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.

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

AW, AB, and AY in the above figure are in a harmonic range.