The Conditional Strong Matching Preclusion of Augmented Cubes

Mohamad Abdallah,Eddie Cheng

doi:10.20429/tag.2021.080105

Abstract

The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube $AQ_n$, which is a variation of the hypercube $Q_n$ that possesses favorable properties.

Highlights

IntroductionIn case of random link failure, it is unlikely to have such situation
A matching in a graph G = (V, E) is a set M of pairwise nonadjacent edges
We have studied the strong matching preclusion problem of augmented cubes under the condition that no isolated vertex is created in the presence of faulty edges and/or vertices

Summary

Introduction

In case of random link failure, it is unlikely to have such situation For this reason, Cheng et al.[6] introduced the conditional matching preclusion which removes from consideration the case when the matching preclusion set produces a graph with an isolated vertex after the edge deletion. Park and Ihm [16] introduced the concept of strong matching preclusion where the matching preclusion set contains vertices and/or edges. This concept corresponds to the situation when the failure of network occurs through nodes and communication lines. The strong matching preclusion set of G is a set of vertices and/or edges whose deletion leads to an unmatchable graph.

Preliminaries

Main Result

Conclusion