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Published in:
24-06-2023
Component edge connectivity and extra edge connectivity of alternating group networks
Published in: The Journal of Supercomputing | Issue 1/2024
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Abstract
The l-component edge connectivity of a graph G, denoted by \({c\lambda _l (G)}\), is the minimum number of edges whose removal from G results in a disconnected graph with at least l-components. The h-extra edge connectivity of a graph G, denoted by \(\lambda _h(G)\), is the minimum number of edges whose removal from G results in a disconnected graph and each component has at least \(h+1\) vertices. In this paper, we determine the l-component edge connectivity and the h-extra edge connectivity of alternating group networks for some small values. For l-component edge connectivity, we prove that \(c\lambda _3(AN_n)=2n-3\) for \(n\ge 3\), \(c\lambda _4(AN_n)=3n-6\) for \(n\ge 4\), and \(c\lambda _5(AN_n)=4n-8\) for \(n\ge 4\). For h-extra edge connectivity, we prove that \(\lambda _1(AN_n)=2n-4\), \(\lambda _2(AN_n)=3n-9\) and \(\lambda _3(AN_n)=4n-12\) for \(n\ge 6\).