The $g$-good neighbor conditional diagnosability of locally exchanged twisted cubes

TL;DR

This paper investigates the fault tolerance of locally exchanged twisted cubes by determining their $g$-good neighbor conditional diagnosability and $R^g$-vertex-connectivity, providing new insights into their reliability under specific models.

Contribution

It introduces the $g$-good neighbor conditional diagnosability for locally exchanged twisted cubes and calculates these parameters under the PMC and MM* models, advancing understanding of their fault tolerance.

Findings

Determined the $R^g$-vertex-connectivity of $LeTQ(s,t)$.

Established the $g$-good neighbor conditional diagnosability under PMC and MM* models.

Provides theoretical bounds for fault tolerance in these network topologies.

Abstract

Connectivity and diagnosability are important parameters in measuring the fault tolerance and reliability of interconnection networks. The $R^g$-vertex-connectivity of a connected graph $G$ is the minimum cardinality of a faulty set $X\subseteq V(G)$ such that $G-X$ is disconnected and every fault-free vertex has at least $g$ fault-free neighbors. The $g$-good-neighbor conditional diagnosability is defined as the maximum cardinality of a $g$-good-neighbor conditional faulty set that the system can guarantee to identify. The interconnection network considered here is the locally exchanged twisted cube $LeTQ(s,t)$. For $1\leq s\leq t$ and $0\leq g\leq s$, we first determine the $R^g$-vertex-connectivity of $LeTQ(s,t)$, then establish the $g$-good neighbor conditional diagnosability of $LeTQ(s,t)$ under the PMC model and MM$^*$ model, respectively.