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