t/t -Diagnosability of regular graphs under the PMC model

Abstract

A system is t/t -diagnosable if, given any collection of test results, the faulty nodes can be isolated to within a set of at most t nodes provided that the number of faulty nodes does not exceed t . Given an N -vertex graph G that is regular with the common degree d and has no cycle of three or four vertices, this study shows that G is (2d − 2)/(2d − 2) -diagnosable if N ≥ 4 d − 30 > 0. Based on this result, the t/t -diagnosabilities of several classes of graphs can be computed efficiently.