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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Bibliographic Details
Published in:Mathematics (Basel) Vol. 12; no. 14; p. 2175
Main Author: Rather, Bilal Ahmad
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.07.2024
Subjects:
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
United Arab Emirates
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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).
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content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math12142175