Perfect codes in proper intersection power graphs of finite groups

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-09-21 DOI:10.1007/s00200-023-00626-2

Xuanlong Ma, Lan Li, Guo Zhong

引用次数: 0

Abstract

Given a finite group G with the identity e, the proper intersection power graph of G is the graph with vertex set \(G\setminus \{e\}\), in which two distinct vertices x and y are adjacent if \(\langle x\rangle \cap \langle y\rangle \) is non-trivial. In this paper, we give a necessary and sufficient condition for a proper intersection power graph to contain a perfect code. As applications, we classify all finite nilpotent groups whose proper intersection power graphs admit a perfect code. We also classify a few classes of finite non-nilpotent groups whose proper intersection power graphs admit a perfect code, such as, symmetric groups and alternating groups.

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有限群的适当交幂图中的完备码

给定一个恒等式为e的有限群G，如果\(\langle x\rangle \cap \langle y\rangle \)是非平凡的，则G的固有交幂图是顶点集\(G\setminus \{e\}\)的图，其中两个不同的顶点x和y相邻。本文给出了一个合适的交点幂图包含一个完美码的充分必要条件。作为应用，我们对其固有交幂图有完美码的所有有限幂零群进行了分类。我们还分类了一些有限非幂零群，它们的固有交幂图承认一个完美码，如对称群和交替群。

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

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.