The Complexity of Power Graphs Associated With Finite Groups

  • Steve Kirkland University of Manitoba
  • Ali Reza Moghaddamfar Faculty of Mathematics, K.N. Toosi University of Technology
  • S. Navid Salehy Department of Mathematics, Florida State University
  • S. Nima Salehy Department of Mathematics, Florida State University
  • Mahsa Zohouratar Faculty of Mathematics, K.N. Toosi University of Technology
Keywords: Power graph, spanning tree, complexity, group.

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.

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Published
2018-12-31
Section
Articles