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Preliminaries.- Incidence Matrix.- Adjacency Matrix.- Laplacian Matrix.- Cycles and Cuts.- Regular Graphs.- Line Graph of a Tree.- Algebraic Connectivity.- Distance Matrix of a Tree.- Resistance… (More)

Theory of permanents provides an effective tool in dealing with order statistics corresponding to random variables which are independent but possibly nonidentically distributed. This is illustrated… (More)

A block graph is a graph in which every block is a complete graph. Let be a block graph and let be the adjacency matrix of . We first obtain a formula for the determinant of over reals. It is shown… (More)

In this article we provide a combinatorial description of an arbitrary minor of the Laplacian matrix (L) of a mixed graph (a graph with some oriented and some unoriented edges). This is a generalized… (More)

Abstract We consider the asymptotics of the Perron eigenvalue and eigenvector of irreducible nonnegative matrices whose entries have a geometric dependance in a large parameter. The first term of the… (More)

Suppose X=(X1,..,Xp)', has the Laplace transform ψ (t) = ∣Ι + VT∣-½, where V is a positive definite matrix and T= diag(t1,..,tp). It is shown that ψ(t) is infinitely divisible if and only if DV-1 D… (More)

Abstract If A an n × n nonnegative, irreducible matrix, then there exists μ ( A ) > 0, and a positive vector x such that max j a ij x j = μ ( A ) x i , i = 1, 2,…, n . Furthermore, μ ( A ) is the… (More)

The max-plus semiring Rmax is the set R∪{−∞}, equipped with the addition (a, b) 7→ max(a, b) and the multiplication (a, b) 7→ a + b. The identity element for the addition, zero, is −∞, and the… (More)

Abstract If Ak=(akij), k= 1,2,…,n, are n-by-n matrices, then their mixed discriminant D(A1,…,An) is given by D(A 1 ,…,A n = 1 n! ∑ σϵS n a σ(j) ij , where Sn is the symmetric group of degree n and… (More)

It is shown that if G is a graph with an odd number of spanning trees, then the line graph L(G) of G has nullity at most one.