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There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

Let lim stand for the limit lim_(x->c), lim_(x->c^-), lim_(x->c^+), lim_(x->infty), or lim_(x->-infty), and suppose that lim f(x) and lim g(x) are both zero or are both ...

There are several sorts of graphs referred to as "star graphs" in mathematics, computer science, and information processing. The most common sort of star is the n-star graph ...

The number of cells in a generalized Chinese checkers board (or "centered" hexagram). Unlike the polygonal numbers, there is ambiguity in the case of the star numbers as to ...

An n×n complex matrix A is called indefinite if nonzero vectors x and y exist such that x^*Ax>0>y^*Ay, where x^* denotes the conjugate transpose. A matrix m may be tested to ...

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...

A polynomial with matrix coefficients. An nth order matrix polynomial in a variable t is given by P(t)=A_0+A_1t+A_2t^2+...+A_nt^n, where A_k are p×p square matrices.

A negative semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonpositive. A matrix m may be tested to determine if it is negative semidefinite in the ...

A nonpositive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a nonpositive number, i.e., a_(ij)<=0 for all i, j. Nonpositive matrices are ...

The subdiagonal of a square matrix is the set of elements directly under the elements comprising the diagonal. For example, in the following matrix, the diagonal elements are ...