We prove that if the direct product of two connected bipartite graphs has isomorphic components, then one of the factors admits an automorphism that interchanges its partite sets. This proves a conjecture made by Jha, Klavžar and Zmazek in 1997 [P. Jha, S. Klavzar, B. Zmazek, Isomorphic components of Kronecker product of bipartite graphs, Discussiones Mathematicae Graph Theory 17 (1997) 302–308...

In this article, we present results on Toeplitz matrices with Oresme numbers components. First, the components are created and then Frobenius(Euclidian), row column norms of these found. Furthermore lower upper bounds obtained for spectral matrices. addition, Frobenius Kronecker Hadamard product calculated.

How can we generate realistic networks? In addition, how can we do so with a mathematically tractable model that allows for rigorous analysis of network properties? Real networks exhibit a long list of surprising properties: Heavy tails for the inand out-degree distribution, heavy tails for the eigenvalues and eigenvectors, small diameters, and densification and shrinking diameters over time. C...

How can we generate realistic networks? In addition, how can we do so with a mathematically tractable model that allows for rigorous analysis of network properties? Real networks exhibit a long list of surprising properties: Heavy tails for the inand out-degree distribution; heavy tails for the eigenvalues and eigenvectors; small diameters; and densification and shrinking diameters over time. T...

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.

Exponential time integrators are well-established discretization methods for semilinear systems of ordinary differential equations. These use ? ? functions, which matrix functions related to the exponential. This work introduces an algorithm speed up computation function action over vectors two-dimensional (2D) matrices expressed as a Kronecker sum. For that, we present auxiliary exponential-re...