We characterize the graphs which achieve the maximum value of the spectral radius of the adjacency matrix in the sets of all graphs with a given domination number and graphs with no isolated vertices and a given domination number. AMS Classification: 05C35, 05C50, 05C69

The natural linear programming formulation of the maximum s-t-flow problem in path variables has a dual linear program whose underlying polyhedron is the dominant P↑ s-t-cut of the s-t-cut polytope. We present a complete characterization of P↑ s-t-cut with respect to vertices, facets, and adjacency.

Let G be a graph of order n and size m, and let mck (G) be the maximum size of a k-cut of G. It is shown that mck (G) k 1 k m μmin (G) n 2 , where μmin (G) is the smallest eigenvalue of the adjacency matrix of G. An infinite class of graphs forcing equality in this bound is constructed.

Superscalar processors are well suited for meeting the demands of scientific computing, given sufficient memory bandwidth. Employing parallel memory modules increases the bandwidth available; however , storage schemes devised to reduce module conflict for vector computers are not suitable for scalar computation. Access ordering is a compilation technique that increases effective bandwidth by re...

The natural linear programming formulation of the maximum s-t-flow problem in path variables has a dual linear program whose underlying polyhedron is the dominant P↑ s-t-cut of the s-t-cut polytope. We present a complete characterization of P↑ s-t-cut with respect to vertices, facets, and adjacency.

For a simple hypergraph H on n vertices, its Estrada index is defined as [Formula in text], where λ 1, λ 2,…, λ n are the eigenvalues of its adjacency matrix. In this paper, we determine the unique 3-uniform linear hypertree with the maximum Estrada index.

Let ∆(G), ∆ for short, be the maximum degree of a graph G. In this paper, trees (resp., unicyclic graphs and bicyclic graphs), which attain the first and the second largest spectral radius with respect to the adjacency matrix in the class of trees (resp., unicyclic graphs and bicyclic graphs) with n vertices and the maximum degree ∆, where ∆ ≥ n+1 2 (resp., ∆ ≥ n 2 +1 and ∆ ≥ n+3 2 ) are determ...

Doctors and clients sometimes experience interactive clashes during hospital meetings in South-western Nigerian hospitals because of their divergent culture-constrained orientation to politeness cues. The goal of this paper is to unpack the discursive elements that characterize interactive confluence and divergence in selected consultative encounters in the hospitals. The findings indicate that...

Let T be a tree, A its adjacency matrix, and a scalar. We describe a linear-time algorithm for reducing the matrix In +A. Applications include computing the rank of A, nding a maximum matching in T , computing the rank and determinant of the associated neighborhood matrix, and computing the characteristic polynomial of A.