Component Edge Connectivity Of Hypercubes
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE(2018)
摘要
Fault tolerance is an important issue in interconnection networks, and the traditional edge connectivity is an important measure to evaluate the robustness of an interconnection network. The component edge connectivity is a generalization of the traditional edge connectivity. The g-component edge connectivity c lambda(g)(G) of a non-complete graph G is the minimum number of edges whose deletion results in a graph with at least g components. Let g be an integer and g = Sigma(s)(i=0) 2t(i) be the decomposition of g such that t(0) = [log(2)g], and t(i) = [log(2)(g -Sigma(i-1)(r=0)-2t(r))] for i >= 1. In this note, we determine the g-component edge connectivity of the hypercube Q(n), c lambda(g) (Q(n)) = ng - (Sigma(s)(i=0) t(i)2t(i)-1 + Sigma(s)(i=0) i center dot 2t(i)) for g <= 2([n/2]) + 1, n >= 7. Moreover, we classify the corresponding optimal solutions.
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关键词
Networks, hypercube, fault-tolerance, component connectivity, component edge connectivity
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