On the diameter of the Kronecker product graph

TL;DR

This paper derives a formula to compute the diameter of the Kronecker product of two graphs using their diameters and primitive exponents, providing a theoretical tool for analyzing such graph products.

Contribution

It introduces a new formula for calculating the diameter of Kronecker product graphs based on properties of the factor graphs, advancing theoretical understanding.

Findings

Provides a formula for the diameter of Kronecker product graphs

Relates the diameter to the diameters and primitive exponents of factor graphs

Enhances theoretical analysis of graph products

Abstract

Let $G_1$ and $G_2$ be two undirected nontrivial graphs. The Kronecker product of $G_1$ and $G_2$ denoted by $G_1\otimes G_2$ with vertex set $V(G_1)\times V(G_2)$, two vertices $x_1x_2$ and $y_1y_2$ are adjacent if and only if $(x_1,y_1)\in E(G_1)$ and $(x_2,y_2)\in E(G_2)$. This paper presents a formula for computing the diameter of $G_1\otimes G_2$ by means of the diameters and primitive exponents of factor graphs.