Vulnerability assessment of a new class of Cayley graph

As the number of links and processors in an interconnection network increases, faulty links and processors are constantly emerging. When a network fails, how to evaluate the state of the network and mitigate the vulnerability of the network itself is the focus of attention in recent years. Therefore, the parameters for assessing network vulnerability have received considerable attention. In general, we use connectivity and diagnosability to reflect the vulnerability of the network. At present, the connectivity and diagnosability of most networks have been determined. In this paper, we mainly analyze Cayley graphs \(EC_m\) $E{C}_m$ , which are generated by disjoint paths with length 2. We explain that connectivity and super connectivity of \(EC_m\) $E{C}_m$ are uniformly 2m, the 1-extra and 3-component connectivity of \(EC_m\) $E{C}_m$ are uniformly \(4m-2\) $4m-2$ . In addition, we also analyze the local diagnosability of \(EC_m\) $E{C}_m$ under the PMC and \(\hbox {MM}^*\) ${\text{MM}}^{\ast }$ models is 2m.