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Fault Tolerance of Cayley Graphs
Shuhong Gao and Beth Novick
Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634- 0975, USA
{sgao, nbeth}@ces.clemson.edu
Annals of Combinatorics 11 (2) p.161-171 June, 2007
AMS Subject Classification: 05C25, 05C40, 68M15
Abstract:
It is a difficult problem in general to decide whether a Cayley graph Cay(G; S) is connected where G is an arbitrary finite group and S a subset of G. For example, testing primitivity of an element in a finite field is a special case of this problem but notoriously hard. In this paper, it is shown that if a Cayley graph Cay(G; S) is known to be connected then its fault tolerance can be determined in polynomial time in |S|log(|G|). This is accomplished by establishing a new structural result for Cayley graphs. This result also yields a simple proof of optimal fault tolerance for an infinite class of Cayley graphs, namely exchange graphs. We also use the proof technique for our structural result to give a new proof of a known result on quasiminimal graphs.
Keywords: Cayley graph, fault tolerance, connectivity

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