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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematics (Basel) Jg. 12; H. 14; S. 2175
1. Verfasser: Rather, Bilal Ahmad
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.07.2024
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
United Arab Emirates
ISSN:2227-7390, 2227-7390
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
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).
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math12142175