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Algebraic Connectivity of Power Graphs of Finite Cyclic Groups

Author

Listed:
  • Bilal Ahmad Rather

    (Department of Mathematical Sciences, College of Science, United Arab Emirate University, Al Ain 15551, United Arab Emirates)

Abstract

The power graph P ( Z n ) of Z n for a finite cyclic group Z n is a simple undirected connected graph such that two distinct nodes x and y in Z n are adjacent in P ( Z n ) if and only if x ≠ y and x i = y or y i = x for some non-negative integer i . In this article, we find the Laplacian eigenvalues of P ( Z n ) and show that P ( Z n ) is Laplacian integral (integer algebraic connectivity) if and only if n is either the product of two distinct primes or a prime power. That answers a conjecture by Panda, Graphs and Combinatorics, (2019).

Suggested Citation

  • Bilal Ahmad Rather, 2024. "Algebraic Connectivity of Power Graphs of Finite Cyclic Groups," Mathematics, MDPI, vol. 12(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2175-:d:1433282
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