The main idea of this paper is to provide an algebraic algorithm for constructing symmetric graphs with optimal fault tolerance. For this purpose, we use normal edge-transitive Cayley graphs and the idea of reconstruction question posed by Praeger to present a special factorization of groups which induces a graphical decomposition of normal edge-transitive Cayley graphs to simpler normal edge-transitive Cayley graphs. Then as a consequence of our results, we continue the study of normal edge-transitive Cayley graphs of abelian groups and we show that knowing normal edge-transitive Cayley graphs of abelian p-groups, we can determine all normal edge-transitive Cayley graphs of abelian groups.
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Khosravi, B., Khosravi, B. & Khosravi, B. On Reconstruction of Normal Edge-Transitive Cayley Graphs. Ann. Comb. (2020). https://doi.org/10.1007/s00026-020-00514-3
Mathematics Subject Classification
- Primary 05C25
- Secondary 08A30
- Normal edge-transitive Cayley graphs
- Factorization of groups
- Optimal fault tolerance