Vertex connectivity of the power graph of a finite cyclic group

被引：19

作者：

Chattopadhyay, Sriparna ^{[1
]}

Patra, Kamal Lochan ^{[1
]}

Sahoo, Binod Kumar ^{[1
]}

机构：

[1] HBNI, Natl Inst Sci Educ & Res, Sch Math Sci, At Po Jatni, Bhubaneswar 752050, Odisha, India

来源：

DISCRETE APPLIED MATHEMATICS | 2019年 / 266卷

关键词：

Power graph; Vertex connectivity; Cyclic group; Euler's totient function;

D O I：

10.1016/j.dam.2018.06.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let n = p(1)(n1)p(2)(n2) . . . p(r)(nr), where r, n(1), n(2), . . . , n(r) are positive integers and p(1), p(2), . . . , P-r are distinct prime numbers with p(1) < p(2) < . . . < p(r). For the finite cyclic group C-n, of order n, let P(C-n) be the power graph of C-n and kappa(P(C-n)) be the vertex connectivity of P(C-n). It is known that kappa(P(C-n)) = p(1)(n1) - 1 if r = 1. For r >= 2, we determine the exact value of kappa(P(C-n)) when 2 phi(p(1)p(2) . . . Pr-1) >= P1P2 . . . Pr-1, and give an upper bound for kappa(P(C-n)) when 2 phi(p(1)p(2) . . . Pr-1) < p(1)p(2) . . . Pr-1, which is sharp for many values of n but equality need not hold always. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：259 / 271

页数：13

共 13 条

[11] Power graphs and semigroups of matrices [J].