On the fault diameter and wide diameter of the exchanged 3-ary $n$-cube

TL;DR

This paper investigates the fault diameter and wide diameter of the exchanged 3-ary n-cube, providing bounds that enhance understanding of its fault tolerance and transmission efficiency in network design.

Contribution

It establishes bounds for the fault and wide diameters of the exchanged 3-ary n-cube, a recent network topology variant, advancing theoretical knowledge in interconnection network analysis.

Findings

Fault diameter bounded between n+3 and n+5

Wide diameter bounded between n+3 and n+5

Results applicable for 1 ≤ r ≤ s ≤ t

Abstract

Fault diameter and wide diameter are two critical parameters for evaluating communication performance in interconnection networks. They measure the fault tolerance and transmission efficiency of networks. The exchanged 3-ary $n$-cube is a recently proposed variant of the hypercube, denoted by $E3C(r, s, t)$. In this work, we obtain that the $(2r + 1)$-fault diameter and $(2r + 2)$-wide diameter of $E3C(r, s, t)$ are bounded between $n + 3$ and $n + 5$ for $1 \leq r \leq s \leq t$.