On Reconstruction of Normal Edge-Transitive Cayley Graphs

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 i...

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Bibliographic Details
Published in:Annals of combinatorics 2020-12, Vol.24 (4), p.791-807
Main Authors: Khosravi, Behnam, Khosravi, Behrooz, Khosravi, Bahman
Format: Article
Language:English
Subjects:
Algorithms
Combinatorics
Fault tolerance
Graphs
Group theory
Mathematics
Mathematics and Statistics
Reconstruction
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Summary: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.
ISSN:0218-0006
0219-3094
DOI:10.1007/s00026-020-00514-3