Metric dimension and strong metric dimension in annihilator-ideal graphs

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

Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-04-20 DOI:10.1007/s00200-024-00657-3

R. Shahriyari, R. Nikandish, A. Tehranian, H. Rasouli

引用次数: 0

Abstract

Let R be a commutative ring with identity and A(R) be the set of ideals with non-zero annihilator. The annihilator-ideal graph of R is defined as the graph \(\mathrm{A_I}(R)\) with the vertex set \(A(R)^*=A(R)\setminus \{0\}\) and two distinct vertices L, K are adjacent if and only if \(\textrm{Ann}_R(K) \cup \textrm{Ann}_R(L)\) is a proper subset of \(\textrm{Ann}_R(KL)\). In this paper, we determine the metric dimension of \(\mathrm{A_I}(R)\). Also, the twin-free clique number for \(\mathrm{A_I}(R)\) is computed and as an application the strong metric dimension in annihilator-ideal graphs is given.

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湮没者理想图中的度量维度和强度量维度

让 R 是一个具有同一性的交换环，A(R) 是具有非零湮没子的理想集。R 的湮没ideal 图定义为顶点集为 A(R)^*=A(R)\setminus \{0\}\)的图 \(\mathrm{A_I}(R)\)和两个不同顶点 L. K 相邻、当且仅当\(textrm{Ann}_R(K) \cup \textrm{Ann}_R(L)\)是\(\textrm{Ann}_R(KL)\)的适当子集时，K 是相邻的。在本文中，我们确定了 \(\mathrm{A_I}(R)\) 的度量维度。同时，我们还计算了 \(\mathrm{A_I}(R)\) 的无孪生簇数，并给出了湮没者理想图中的强度量维度。

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.