Conditional Fault Hamiltonicity of the Star Graph

Abstract

Fault tolerance is an important property of network performance. A graph \(G\) is \(k\)-edge-fault conditional Hamiltonian if \(G – F\) is Hamiltonian for every \(F \subset E(G)\) with \(|F| \leq k\) and \(\delta(G – F) \geq 2\). In this paper, we show that for \(n \geq 4\), the \(n\)-dimensional star graph \(S_n\) is \((3n – 10)\)-edge-fault conditional Hamiltonian.