given a graph $g$, let $g^sigma$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^sigma)$. then the spectrum of $s(g^sigma)$ consisting of all the eigenvalues of $s(g^sigma)$ is called the skew-spectrum of $g^sigma$, denoted by $sp(g^sigma)$. the skew energy of the oriented graph $g^sigma$, denoted by $mathcal{e}_s(g^sigma)$, is defined as the sum of the n...

in this paper, we present a numerical algorithm for solving matrix equations $(a otimes b)x = f$  by extending the well-known gaussian elimination for $ax = b$. the proposed algorithm has a high computational efficiency. two numerical examples are provided to show the effectiveness of the proposed algorithm.

Stochastic Kronecker Product Graphs are an interesting and useful class of Generative Network Models. They can be fitted using a fast Maximum Likelihood Estimator and reproduce many important statistical properties commonly found in large real-world networks. However, they suffer from an unfortunate drawback: the need to pad the Stochastic Kronecker Product Graph with isolated vertices. To addr...

In this paper, we investigate isomorphic factorizations of the Kronecker product graphs. Using these relations, it is shown that (1) the Kronecker product of the d-out-regular digraph and the complete symmetric digraph is factorized into the line digraph, (2) the Kronecker product of the Kautz digraph and the de Bruijn digraph is factorized into the Kautz digraph, (3) the Kronecker product of b...

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...

In this paper, first we convert the non-linear matrix Lyapunov system into a Kronecker product matrix system with the help of Kronecker product of matrices. Then, we obtain sufficient conditions for Ψasymptotic stability and Ψ-uniform stability of the trivial solutions of the corresponding Kronecker product system. c ©2012 NGA. All rights reserved.