Abstract
The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. Park and Ihm introduced the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. In this paper, we find the conditional strong matching preclusion number for the $n$-dimensional alternating group graph $AG_n$.
Highlights
IntroductionA trivial case of matching preclusion occurs when all edges in G incident to a single vertex are deleted when G has even number of vertices, or when all edges in G incident to two particular vertices are deleted when G has an odd number of vertices
Given a graph G = (V, E), a set M of pairwise nonadjacent edges is called matching
We find the conditional strong matching preclusion number for the n-dimensional alternating group graph AGn
Summary
A trivial case of matching preclusion occurs when all edges in G incident to a single vertex are deleted when G has even number of vertices, or when all edges in G incident to two particular vertices are deleted when G has an odd number of vertices This case models a situation where link failures are concentrated at only a very few nodes of a communication network. When such case is unlikely to happen, Cheng et al [10] introduced a useful notion called 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. Theory and Applications of Graphs, Vol 6 [2019], Iss. 2, Art. 5 group graph AGn, which is the minimum size of all conditional strong matching preclusion sets of AGn
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