Diameter formulas for a class of undirected multi-loop networks

TL;DR

This paper derives formulas for the diameter of a specific class of undirected multi-loop networks and explores their relationship with generalized Petersen graphs.

Contribution

It provides explicit diameter formulas for multi-loop networks with a fixed first step size and links these diameters to those of generalized Petersen graphs.

Findings

Derived diameter formulas for multi-loop networks with s_1=1

Established a relation between multi-loop network diameters and generalized Petersen graphs

Enhanced understanding of network topology and routing efficiency

Abstract

Let $n\geq 5$ and $m\geq 1$ be positive integers. Let $S = ( s_1, s_2, \ldots , s_m)$ be a sequence of integers such that $1 \leq s_1 < s_2 < \ldots < s_m \leq \lfloor \frac{n-1}{2} \rfloor.$ In this paper, we discuss the diameter of multi-loop networks $C_n(s_1,s_2, \ldots, s_m)$ when $s_1=1$. We also present a relation between the diameter of multi-loop networks and the diameter of generalized Petersen graphs.