A note on the strong matching preclusion problem for data center networks

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. The class of data center networks has been proposed as a good class of models in the design of computer networks. Such a data center network can be viewed as a server-centric interconnection network structure, which can support millions of servers with high network capacity that uses only commodity switches. In this paper, we determine the strong matching preclusion number of k-dimensional data center networks with n-port switches and tk,n servers for k≥0 and n≥2. In addition, optimal strong matching preclusion sets of these graphs are categorized.