1. The High Faulty Tolerant Capability of the Alternating Group Graphs.
- Author
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Zhang, Hui, Hao, Rong-Xia, Qin, Xiao-Wen, Lin, Cheng-Kuan, and Hsieh, Sun-Yuan
- Subjects
FAULT tolerance (Engineering) ,WIRELESS communications - Abstract
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 $AG_{n}$ A G n , the structure properties and (conditional) matroidal connectivity are studied based on the dimensional partition of $E(AG_{n})$ E (A G n) . We prove that for $S\subseteq E(AG_{n})$ S ⊆ E (A G n) under some limitation on the number of faulty edges in each dimensional edge set, if $|S|\leq (n-1)!-1$ | S | ≤ (n - 1) ! - 1 , then $AG_{n}-S$ A G n - S is connected. We study the value of matroidal connectivity and conditional matroidal connectivity of $AG_{n}$ A G n . Furthermore, simulations have been carried out to compare the matroidal connectivity with other types of conditional connectivity in $AG_{n}$ A G n . The simulation result shows that the matroidal connectivity significantly improves these known fault-tolerant capability of alternating group graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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