Algebraic Connectivity of Power Graphs of Finite Cyclic Groups

Algebraic Connectivity of Power Graphs of Finite Cyclic Groups

The power graph P(Zn) of Zn for a finite cyclic group Zn is a simple undirected connected graph such that two distinct nodes x and y in Zn are adjacent in P(Zn) if and only if x≠y and xi=y or yi=x for some non-negative integer i. In this article, we find the Laplacian eigenvalues of P(Zn) and show t...

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Veröffentlicht in:Mathematics (Basel) 2024-07, Vol.12 (14), p.2175
1. Verfasser: Rather, Bilal Ahmad
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
algebraic connectivity
Analysis
Combinatorial analysis
Connectivity
Eigenvalues
Euler’s totient function
Graph theory
Graphs
Group theory
Integers
integers modulo group
Laplacian integral
Laplacian matrix
power graphs
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Zusammenfassung:The power graph P(Zn) of Zn for a finite cyclic group Zn is a simple undirected connected graph such that two distinct nodes x and y in Zn are adjacent in P(Zn) if and only if x≠y and xi=y or yi=x for some non-negative integer i. In this article, we find the Laplacian eigenvalues of P(Zn) and show that P(Zn) 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).
ISSN:2227-7390
2227-7390
DOI:10.3390/math12142175