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...

it is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. in this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.

let $r$ be a commutative ring. in this paper, by using algebraic properties of $r$, we study the hase digraph of prime ideals of $r$.

In this note, we give a characterization of the adjacency matrix of the line digraph of a regular digraph and we discuss a generalization.On the light of the characterization given, we remark that the underlying digraph of a coined quantum random walk is the line digraph of a regular digraph. 1. A characterization of the adjacency matrix of the line digraph of a regular digraph 1.1. Set-up. The...

This paper addresses the problem of distributed optimization, where a network agents represented as directed graph (digraph) aims to collaboratively minimize sum their individual cost functions. Existing approaches for optimization over digraphs, such Push-Pull, require exchange explicit state values with neighbors in order reach an optimal solution. However, this can result disclosure sensitiv...

Hamming claimed Òthe purpose of computing is insight, not numbers.Ó In a variant of that aphorism, we show how the Virtual Reality Modeling Language (VRML) can provide powerful insight into the mathematical properties of numbers. The mathematical problem we consider is the relatively recent conjecture colloquially known as the "3x + 1 problem". It refers to an iterative integer function that al...

This paper presents results from an investigation regarding the use of the Design Structure Matrix (DSM) as a means to guide a designer through the calculation of numerical relationships within the early design system Designer. Characteristics, relationships and goals are used within Designer to enable the evaluation and approximation of the design model and are represented within the system as...

a kernel $j$ of a digraph $d$ is an independent set of vertices of $d$ such that for every vertex $w,in,v(d),setminus,j$ there exists an arc from $w$ to a vertex in $j.$in this paper, among other results, a characterization of $2$-regular circulant digraph having a kernel is obtained. this characterization is a partial solution to the following problem: characterize circulant digraphs which hav...

Study the relationship between unitary matrices and their patterns is motivated by works in quantum chaology (see, e.g., [KS99]) and quantum computation (see, e.g., [M96] and [AKV01]). We prove that if a Cayley digraph is a line digraph then it is the pattern of a unitary matrix. We prove that for any finite group with two generators there exists a set of generators such that the Cayley digraph...