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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)

R. B. Bapat 2 A. K. Lal3 Sukanta Pati 4 Abstract We consider a q-analogue of the distance matrix (called the q-distance matrix) of an unweighted tree and give formulae for the inverse and the… (More)

If A is an n x n nonnegative, irreducible matrix, then there exists /L(A) > 0. and a positive vector x such that max,a,,x, = &4)x,. i = 1,2. n. Furthermore, ,n(A) is the maximum geometric mean of a… (More)

The resistance distance ri j between two vertices vi and v j of a (connected, molecular) graph G is equal to the effective resistance between the respective two points of an electrical network,… (More)

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