|標題:||CONDITIONAL MATCHING PRECLUSION FOR THE STAR GRAPHS|
Tan, Jimmy J. M.
Department of Computer Science
|關鍵字:||Interconnection networks;perfect matching;star graphs|
|摘要:||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 incident to a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those incident to 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 paper, we find this number and classify all optimal sets for the star graphs, one of the most popular interconnection networks.|