The spectrum of the Laplacian, signless Laplacian and adjacency matrices of the family of the weighted graphs R{H}, obtained from a connected weighted graph R on r vertices and r copies of a modified Bethe tree H by identifying the root of the i-th copy of H with the i-th vertex of R, is determined.

Determining the Fiedler vector of the Laplacian or adjacency matrices of graphs is the most computationally intensive component of several applications, such as graph partitioning, graph coloring, envelope reduction, and seriation. Often an approximation of the Fiedler vector is suÆcient. We discuss issues involved in the use of Monte Carlo techniques for this purpose.

We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are crucial in applications, such as DNA microarrays and sensor networks, where dense measurements are not practically feasible. One possible construction uses ...

Abstract We address the problem of facial expression recognition and show a possible solution using quantum machine learning approach. In order to define an efficient classifier for given dataset, our approach substantially exploits interference. By representing face expressions via graphs, we as circuit that manipulates graphs adjacency matrices encoded into amplitudes some appropriately defin...

We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the first two cases, we compute the spectrum explicitly and show that it is determined by the spectrum of the adjacency matrix of the original graph. We then show ...

In this paper, we consider comparing dynamical systems by using graph matching method either between the graphs representing the underlying symbolic dynamics, or graphs approximating the action of the systems on a fine but otherwise non generating partition. For conjugate systems, the graphs are isomorphic and we show that the permutation matrices that relate the adjacency matrices coincides wi...

Let be a distance-regular graph with adjacency matrix A. Let I be the identity matrix and J the all-1 matrix. Let p be a prime. We study the p-rank of the matrices A + bJ − cI for integral b, c and the p-rank of corresponding matrices of graphs cospectral with . Using the minimal polynomial of A and the theory of Smith normal forms we first determine which p-ranks of A follow directly from the ...