Fractional matching preclusion of fault Hamiltonian graphs

TL;DR

This paper investigates the fractional matching preclusion numbers of fault Hamiltonian graphs, providing exact values for certain classes and applications to well-known networks, enhancing understanding of network robustness.

Contribution

It establishes the fractional matching preclusion and strong matching preclusion numbers for $( ext{delta}-2)$-fault Hamiltonian graphs with minimum degree at least 3, and applies results to known networks.

Findings

Determined FMP and FSMP numbers for specific fault Hamiltonian graphs.

Provided exact values for well-known network topologies.

Enhanced understanding of network robustness under edge and vertex failures.

Abstract

Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. As a generalization of matching preclusion, the fractional matching preclusion number (FMP number for short) of a graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matchings, and the fractional strong matching preclusion number (FSMP number for short) of a graph is the minimum number of edges and/or vertices whose deletion leaves a resulting graph with no fractional perfect matchings. A graph $G$ is said to be $f$-fault Hamiltonian if there exists a Hamiltonian cycle in $G-F$ for any set $F$ of vertices and/or edges with $|F|\leq f$. In this paper, we establish the FMP number and FSMP number of $(\delta-2)$-fault Hamiltonian graphs with minimum degree $\delta\geq 3$. As applications, the FMP number and FSMP number of some well-known networks are determined.