The pessimistic diagnosability of graphs and its applications to four kinds of interconnection networks

ABSTRACT In a simple graph , let be the minimum cardinality of the neighbourhoods of any two adjacent vertices, i.e. . Let be the connectivity of G. In this paper, we prove that the pessimistic diagnosability of G, denoted by , is equal to if the following two conditions hold: (1) for any subset with , ; (2) . As examples of its applications, we prove that the pessimistic diagnosabilities of n-dimensional hypercube-like network , dual-cube , pancake network , and burnt pancake graph are (), (), () and (), respectively.