Fractional Matching Preclusion for Data Center Networks
Abstract
An edge subset of is a fractional matching preclusion set (FMP set for short) if has no fractional perfect matchings. The fractional matching preclusion number (FMP number for short) of , denoted by , is the minimum size of FMP sets of . A set of edges and vertices of is a fractional strong matching preclusion set (FSMP set for short) if has no fractional perfect matchings. The fractional strong matching preclusion number (FSMP number for short) of , denoted by , is the minimum size of FSMP sets of . Data center networks have been proposed for data centers as a server-centric interconnection network structure, which can support millions of servers with high network capacity by only using commodity switches. In this paper, we obtain the FMP number and the FSMP number for data center networks , and show that for , and for , . In addition, all the optimal fractional strong matching preclusion sets of these graphs are categorized.
Communicated by Eddie Cheng
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