On the Connectivity of Enhanced Power Graphs of Finite Groups

被引：20

作者：

Bera, Sudip ^{[1
]}

Dey, Hiranya Kishore ^{[2
]}

Mukherjee, Sajal Kumar ^{[1
]}

机构：

[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

[2] Indian Inst Technol, Dept Math, Bombay, Maharashtra, India

来源：

GRAPHS AND COMBINATORICS | 2021年 / 37卷 / 02期

关键词：

Abelian group; Dominating vertex; Enhanced power graph; Vertex connectivity; ZERO-DIVISOR GRAPH;

D O I：

10.1007/s00373-020-02267-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the vertex connectivity of enhanced power graphs of finite groups. We classify all abelian groups G such that the vertex connectivity of enhanced power graph of G is 1. We derive an upper bound for the vertex connectivity of the enhanced power graph of any general abelian group G. Also we completely characterize all abelian groups G, such that the proper enhanced power graph is connected. Moreover, we study some special class of non-abelian groups G such that the proper enhanced power graph is connected and we find their vertex connectivity.

引用

页码：591 / 603

页数：13

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