Algebraic Connectivity of Power Graphs of Finite Cyclic Groups

被引：1

作者：

Rather, Bilal Ahmad ^{[1
]}

机构：

[1] United Arab Emirate Univ, Coll Sci, Dept Math Sci, Al Ain 15551, U Arab Emirates

来源：

MATHEMATICS | 2024年 / 12卷 / 14期

关键词：

algebraic connectivity; Laplacian matrix; Laplacian integral; power graphs; integers modulo group; Euler's totient function; MATRICES; SPECTRUM;

D O I：

10.3390/math12142175

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 not equal 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).

引用

页数：12

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