The High Faulty Tolerant Capability of the Alternating Group Graphs

The matroidal connectivity and conditional matroidal connectivity are novel indicators to measure the real faulty tolerability. In this paper, for the $n$ -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.