Reliabilities for two kinds of graphs with smaller diameters

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 cor-rectly identify. In this paper, aim to obtain the reliability of various graphs (e.g. inter-connection 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. Further-more, we study their reliabilities, including connectivities and diagnosabilities. Moreover, we also extend our results to many graphs. (c) 2023 Elsevier Inc. All rights reserved.