The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime power p, we determine all integral circu...

We derive the joint limiting distribution for the largest eigenvalues of the adjacency matrix for stochastic blockmodel graphs when the number of vertices tends to infinity. We show that, in the limit, these eigenvalues are jointly multivariate normal with bounded covariances. Our result extends the classical result of Füredi and Komlós on the fluctuation of the largest eigenvalue for Erdős-Rén...

in the present work we use the negativity to study the effect of rashba parameter on the thermal entanglement ofelectronic spin and subband states inside a quasi-one-dimensional rashba nanowire, in a perpendicular uniformmagnetic field. we assume that the nanowire is held at a temperature t, so that both spin and subband states, withdefinite probabilities, are present. the partially transposed ...

We discuss quantum graphs consisting of a compact part and semiinfinite leads. Such a system may have embedded eigenvalues if some edge lengths in the compact part are rationally related. If such a relation is perturbed these eigenvalues may turn into resonances; we analyze this effect both generally and in simple examples. Perturbed quantum graphs with rationally related edges 2

New criteria for which Cayley graphs of cyclic groups of any order can be completely determined–up to isomorphism–by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley graphs of cyclic groups with the same list of eigenvalues of their adjacency matrices will be presented.

Among all simple nonbipartite 2-connected graphs, the minimum least Q-eigenvalues are completely determined. As for θ-graphs known as a special class of also

We consider weighted graphs, where the edgeweights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain an upper bound on the spectral radius of the adjacency matrix and characterize graphs for which the bound is attained. © 2007 Elsevier B.V. All rights reserved.

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. In this study the upper bounds for the spectral radius of weighted graphs, which edge weights are positive definite matrices, are compared. Mathematics Subject Classification: 05C50