Journal
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
Volume 34, Issue 1, Pages 225-233Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPDS.2022.3217415
Keywords
Fault tolerant systems; Matroidal connectivity; conditional matroidal connectivity; alternating group graph; fault tolerance
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This paper investigates the applications of matroidal connectivity and conditional matroidal connectivity in alternating group graphs and proves the connectivity under certain conditions. The experimental results show that the matroidal connectivity significantly improves the fault-tolerant capability of alternating group graphs.
The matroidal connectivity and conditional matroidal connectivity are novel indicators to measure the real faulty tolerability. In this paper, for the $n$n-dimensional alternating group graph $AG_{n}$AGn, the structure properties and (conditional) matroidal connectivity are studied based on the dimensional partition of $E(AG_{n})$E(AGn). We prove that for $S\subseteq E(AG_{n})$S & SUBE;E(AGn) under some limitation on the number of faulty edges in each dimensional edge set, if $|S|\leq (n-1)!-1$|S|& LE;(n-1)!-1, then $AG_{n}-S$AGn-S is connected. We study the value of matroidal connectivity and conditional matroidal connectivity of $AG_{n}$AGn. Furthermore, simulations have been carried out to compare the matroidal connectivity with other types of conditional connectivity in $AG_{n}$AGn. The simulation result shows that the matroidal connectivity significantly improves these known fault-tolerant capability of alternating group graphs.
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