Computing the (forcing) strong metric dimension in strongly annihilating-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 : 2023-04-22 DOI:10.1007/s00200-023-00601-x

M. Pazoki, R. Nikandish

引用次数: 0

Abstract

The strongly annihilating-ideal graph \(\textrm{SAG}(R)\) of a commutative unital ring R is a simple graph whose vertices are non-zero ideals of R with non-zero annihilator and there exists an edge between two distinct vertices if and only if each of them has a non-zero intersection with annihilator of the other one. In this paper, we compute twin-free clique number of \(\textrm{SAG}(R)\) and as an application strong metric dimension of \(\textrm{SAG}(R)\) is given. Moreover, we investigate the structures of strong resolving sets in \(\textrm{SAG}(R)\) to find forcing strong metric dimension in \(\textrm{SAG}(R)\).

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强湮灭理想图中强度量维数的计算

交换一元环R的强湮灭理想图\(\textrm{SAG}(R)\)是一个简单图，它的顶点是具有非零湮灭子的R的非零理想，并且当且仅当两个不同的顶点与另一个的湮灭子有非零相交时，它们之间存在一条边。本文计算了\(\textrm{SAG}(R)\)的无双团数，并给出了\(\textrm{SAG}(R)\)的强度量维数作为应用。此外，我们研究了\(\textrm{SAG}(R)\)中的强解析集的结构，以找到\(\textrm{SAG}(R)\)中的强制强度量维。

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.

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