Reliabilities for two kinds of graphs with smaller diameters

Abstract

Two crucial parameters to be considered when evaluating a network’s reliability are its connectivity and diagnosability. The connectivity of a graph is defined as the smallest number of vertices that, if removed, would leave a disconnected or single-vertex graph. The diagnosability is the maximum number of faulty vertices that the system can correctly identify. In this paper, aim to obtain the reliability of various graphs (e.g. interconnection networks and data center networks), we propose two kinds of graphs (resp. networks)—matching recursive graphs (MRGs) and recursive networks based on connected graphs (RNCGs). We prove that these two kinds of graphs have smaller diameters. Furthermore, we study their reliabilities, including connectivities and diagnosabilities. Moreover, we also extend our results to many graphs.