Nilpotent groups whose difference graphs have positive genus

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-02 DOI:10.1007/s11587-023-00830-9

Parveen, Jitender Kumar

引用次数: 0

Abstract

The power graph of a finite group G is a simple undirected graph with vertex set G and two vertices are adjacent if one is a power of the other. The enhanced power graph of a finite group G is a simple undirected graph whose vertex set is the group G and two vertices a, b are adjacent if there exists \(c \in G\) such that both a and b are powers of c. In this paper, we study the difference graph \(\mathcal {D}(G)\) of a finite group G which is the difference of the enhanced power graph and the power graph of G with all isolated vertices removed. We characterize all the finite nilpotent groups G such that the genus (or cross-cap) of the difference graph \(\mathcal {D}(G)\) is at most 2.

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差分图有正格的幂零群

有限群G的幂图是一个简单的无向图，其顶点集G和两个顶点相邻，如果其中一个是另一个的幂。有限群G的增强幂图是一个简单无向图，其顶点集为群G，且两个顶点a, b相邻，如果存在\(c \in G\)使得a和b都是c的幂。本文研究了有限群G的差分图\(\mathcal {D}(G)\)，该差分图是所有孤立顶点被去掉后增强幂图与G的幂图之差。我们刻画了所有有限幂零群G，使得差分图\(\mathcal {D}(G)\)的属(或交叉帽)不超过2。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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