Lucky edge geometric mean labeling of graphs and applications in electrical networks

Mariaraja, P.; Almngoshi, Hussein Z.; Jerlin, C. M. Hilda; Muthuperumal, S.; Amarendra, K.; Sengan, Sudhakar; Dadheech, Pankaj

doi:10.47974/JDMSC-2086

Open Access Research Article

Lucky edge geometric mean labeling of graphs and applications in electrical networks

P. Mariarajamariarajap@gmail.comDepartment of Electrical and Electronics Engineering P. A. College of Engineering and Technology Pollachi, Tamil Nadu, 642002, IndiaView full profile → , Hussein Z. Almngoshihussein.z@uokerbala.edu.iqDepartment of Computer Science College of Computer Science and Information Technology University of Kerbala ; Department of Information Technology College of Science University of Warith Al-Anbiyaa Department of Computer Science College of Computer Science and Information Technology University of Kerbala Karbala, 56001, IraqView full profile → , C. M. Hilda Jerlinruthjerry97@gmail.comDepartment of Artificial Intelligence and Data Science Panimalar Engineering College Chennai, Tamil Nadu, 600069, IndiaView full profile → , S. Muthuperumalmuthuperumal@krce.ac.inDepartment of Mathematics K. Ramakrishnan College of EngineeringTrichy, Tamil Nadu, 621112, IndiaView full profile → , K. Amarendraamarendra@kluniversity.inDepartment of Computer Science and Engineering Koneru Lakshmaiah Education FoundationVaddeswaram, Andhra Pradesh, 522502, IndiaView full profile → , ^*Sudhakar SenganCorresponding authorsudhasengan@gmail.comDepartment of Computer Science and Engineering PSN College of Engineering and Technology Department of Computer Science and Engineering PSN College of Engineering and TechnologyTirunelveli, Tamil Nadu, 627152, IndiaView full profile → , Pankaj Dadheechpankajdadheech777@gmail.comDepartment of Computer Science and Engineering Swami Keshvanand Institute of Technology, Management & Gramothan (SKIT) Department of Computer Science & Engineering Swami Keshvanand Institute of Technology, Management & GramothanJaipur, Rajasthan, 302017, IndiaView full profile →

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pp. 2133–2141Vol. 27Issue 7October 2024DOI: 10.47974/JDMSC-2086 Crossmark XML

Received:: 07 Mar 2024
Published Online:: 15 Oct 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2086
Pages:: 2133–2141

Abstract

A Lucky Edge Geometric Mean Labeling (LEGML) is a function μ that assigns the integers to the vertices of graph G such that for every edge as ‘{E}’, uv∈E(G) there exists a function μ*:E(G) → N is defined by μ* (uv) = √μ(u)μ(v) (or) √μ(u)μ(v) with the state that μ* (uv) ≠ μ* (vw) whenever {u} and {vw} have a common vertex as {v}. A minor number ‘k→ E = {1, 2, 3 … k} is the LEGML of G and is signified by h¢GM(G). A result that accepts LEGML is the Lucky Edge Geometric Mean Graph (LEGMG). The idea of the Graph Theory (GT) concept is fused into the Electric Circuit (EC), and the related complicated problems are transformed into graph model representation problems; as a result, the valuation method is simplified and optimized. Network analysis means finding the current or voltage in each branch. One application of GT is the representation of EC. An ‘E’ in a diagram can signify anything in an EC. Each part of the diagram can represent a port or a terminal in the EC. In this article, we have to investigate the Middle Graph (MG) of the star, the Total Graph (TG) of the star, and the central graph (CG) of the star, which accepts LEGML and LEGMG. This method also computes the power consumed by all the resistors of the EC by LEGML.

Keywords

Central graph Electrical networks Lucky edge geometric mean Middle graph Star graph Total graph

Subject Classifications

05C78

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