The Pessimistic Diagnosabilities Of Some General Regular Graphs

The pessimistic diagnosis strategy is a classic strategy based on the PMC model. A system is t/t-diagnosable if, provided the number of faulty processors is bounded by t, all faulty processors can be isolated within a set of size at most t with at most one fault-free node mistaken as a faulty one. The pessimistic diagnosability of a system G, denoted by t(p)(G), is the maximal number of faulty processors so that the system G is t/t-diagnosable. In this paper, we study the pessimistic diagnosabilities of some general k-regular k-connected graphs G(n). The main result t(p)(G(n)) = 2k - 2 - g under some conditions is obtained, where g is the maximum number of common neighbors between any two adjacent vertices in Gn. As applications of the main result, every pessimistic diagnosability of many famous networks including some known results, such as the alternating group networks AN(n), the k-ary n-cubes Q(n)(k), the star graphs S-n, the matching composition networks G(G(1), G(2); M) and the alternating group graphs AG(n), are obtained. (C) 2015 Elsevier B.V. All rights reserved.