差分图有正格的幂零群

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

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引用次数: 0

摘要

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。

Nilpotent groups whose difference graphs have positive genus

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Nilpotent groups whose difference graphs have positive genus

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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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.