Conditional Matching Preclusion for the Alternating Group Graphs and Split-Stars
International Journal of Computer Mathematics
1120 - 1136
Taylor & Francis
The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this article we find this number and classify all optimal sets for the alternating group graphs, one of the most popular interconnection networks, and their companion graphs, the split-stars. Moreover, some general results on the conditional matching problem are presented.
interconnection networks, perfect matching, alternating group graphs, split-stars
Computer Sciences | Discrete Mathematics and Combinatorics | Mathematics | OS and Networks
Marc Lipman (2011).
Conditional Matching Preclusion for the Alternating Group Graphs and Split-Stars. International Journal of Computer Mathematics.88 (6), 1120 - 1136. Taylor & Francis.