The High Faulty Tolerant Capability of the Alternating Group Graphs
Hui Zhang, Rong‐Xia Hao, Xiao-Wen Qin, Cheng‐Kuan Lin, Sun‐Yuan Hsieh · IEEE Transactions on Parallel and Distributed Systems · 2022
The matroidal connectivity and conditional matroidal connectivity are novel indicators to measure the real faulty tolerability. In this paper, for the$n$-dimensional alternating group graph$AG_{n}$, the structure properties and (conditional) matroidal connectivity are studied based on the dimensional partition of$E(AG_{n})$. We prove that for$S\subseteq E(AG_{n})$under some limitation on the number of faulty edges in each dimensional edge set, if$|S|\leq (n-1)!-1$, then$AG_{n}-S$is connected. We study the value of matroidal connectivity and conditional matroidal connectivity of$AG_{n}$. Furthermore, simulations have been carried out to compare the matroidal connectivity with other types of conditional connectivity in$AG_{n}$. The simulation result shows that the matroidal connectivity significantly improves these known fault-tolerant capability of alternating group graphs.