Abstract
For a finite group G, the power graph of G, denoted by P(G), is a special type undirected graph which has the group elements as its vertex set and two distinct vertices are adjacent if one is non-negative power of other. In this paper, we are interested in the extreme vertices of the power graph P(G) of a finite group G. We determine whether a vertex of P(G) is extreme vertex or not if G is permutation group on n symbols using the concept of disjoint cyclic decomposition of vertex as element of permutation group on n symbols.
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Acknowledgements
This work was supported by UGC, New Delhi under junior research fellowship UGC-Award No: 201610002863 through the first author and CSIR, New Delhi under junior research fellowship CSIR-Award No: 09/382(0229)/2019-EMR-I through the second author.
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Kumari, U., Yadav, R., Sehgal, A. et al. The extreme vertices of the power graph of group \(S_n\). J. Appl. Math. Comput. 69, 3835–3849 (2023). https://doi.org/10.1007/s12190-023-01906-3
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DOI: https://doi.org/10.1007/s12190-023-01906-3