The extreme vertices of the power graph of group Sn

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 grap...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2023-10, Vol.69 (5), p.3835-3849
Main Authors: Kumari, Usha, Yadav, Renu, Sehgal, Amit, Mehra, Seema
Format: Article
Language:English
Subjects:
Apexes
Computational Mathematics and Numerical Analysis
Graph theory
Group theory
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Permutations
Symbols
Theory of Computation
Vertex sets
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Summary: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.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-023-01906-3