Journal
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
Volume 33, Issue 1, Pages 33-43Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129054121500349
Keywords
Cayley graph; largest component; strong Menger (edge) connectivity; transposition tree
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Funding
- General Project of Hunan Provincial Education Department of China [19C1742]
- Youth Project of Hunan Provincial Natural Science Foundation of China [2021JJ40522, 2019RS1057]
- Project of Scientific Research Fund of Hunan Provincial Science and Technology Department [2018WK4006]
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This paper investigates the Cayley graph generated by a transposition tree and identifies the maximum edge and vertex fault tolerance with respect to the strong Menger connectivity. The results extend or improve upon previous research on this topic.
The Cayley graph generated by a transposition tree Gamma(n) is a class of Cayley graphs that contains the star graph and the bubble sort graph. A graph G is called strongly Menger (SM for short) (edge) connected if each pair of vertices x,y are connected by min{d(G)(x),d(G)(y)} (edge)-disjoint paths, where d(G)(x),d(G)(y) are the degree of x and y respectively. In this paper, the maximally edge-fault-tolerant and the maximally vertex-fault-tolerant of Gamma(n) with respect to the SM-property are found and thus generalize or improve the results in [19, 20, 22, 26] on this topic.
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