The Complexity of Power Graphs Associated With Finite Groups

Steve Kirkland, Ali Reza Moghaddamfar, S. Navid Salehy, S. Nima Salehy, Mahsa Zohouratar

Abstract


The power graph P(G) of a finite group G is the graph whose vertex set is
G, with two elements in G being adjacent if one of them is a power of the
other. The purpose of this paper is twofold: (1) to find the complexity of
a clique-replaced graph and study some applications; (2) to derive some
explicit formulas concerning the complexity \kappa(P(G)) for various groups
G such as the cyclic group of order n, the simple groups L_2(q), the extra-
special p-groups of order p^3, the Frobenius groups, etc.


Keywords


Power graph, spanning tree, complexity, group.

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DOI: https://doi.org/10.11575/cdm.v13i2.62733

DOI (PDF): https://doi.org/10.11575/cdm.v13i2.62733.g46830

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Contributions to Discrete Mathematics. ISSN: 1715-0868