Characterization of groups with planar, toroidal or projective planar (proper) reduced power graphs

被引：11
|
作者：
Anitha, T. [1 ]
Rajkumar, R. [1 ]
机构：
[1] Gandhigram Rural Inst Deemed Be Univ, Dept Math, Gandhigram 624302, Tamil Nadu, India
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 05期
关键词：
Group; reduced power graph; planar graph; toroidal graph; projective planar graph; KURATOWSKI THEOREM; GENUS;
D O I：
10.1142/S0219498820500991
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The reduced power graph RP(G) of a group G is the graph whose vertex set is the set of all elements of G, and two vertices u and v are adjacent in RP(G) if and only if < u > subset of < v > or < v > subset of < u >. The proper reduced power graph RP*(G) is the subgraph of RP(G) induced by the set of all nontrivial elements of G. In this paper, we study the planarity, toroidality and projective planarity of (proper) reduced power graph of a group.
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页数：16
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