Wiener index of C6C4 mesh topology

Rajalaxmi, T. M.; Sailusha, P. B.; Samiullah, Maahirah; Arputhaselvi, R.; Christy, C. Jenisha

doi:10.47974/JDMSC-2572

Open Access Research Article

Wiener index of C6C4 mesh topology

^*T. M. RajalaxmiCorresponding authorlaxmi.raji18@gmail.comDepartment of Mathematics Sri Sivasubramaniya Nadar College of EngineerinDepartment of Mathematics Sri Sivasubramaniya Nadar College of EngineeringChennai, Tamil Nadu, 603110, India0000-0001-9700-8110View full profile → , P. B. Sailushapbsailusha@gmail.comDepartment of Mathematics Sri Sivasubramaniya Nadar College of EngineeringChennai, Tamil Nadu, 603110, IndiaView full profile → , Maahirah Samiullahmaahirah2110902@ssn.edu.inDepartment of Chemical Engineering Sri Sivasubramaniya Nadar College of EngineeringChennai, Tamil Nadu, 603110, IndiaView full profile → , R. Arputhaselviarputhaselvi2110528@ssn.edu.inDepartment of Chemical Engineering Sri Sivasubramaniya Nadar College of EngineeringChennai, Tamil Nadu, 603110, IndiaView full profile → , C. Jenisha Christyjenishachristy2110904@ssn.edu.inDepartment of Chemical Engineering Sri Sivasubramaniya Nadar College of EngineeringChennai, Tamil Nadu, 603110, IndiaView full profile →

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pp. 1883–1893Vol. 29Issue 4April 2026DOI: 10.47974/JDMSC-2572 Crossmark XML

Received:: 01 May 2025
Published Online:: 08 Apr 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2572
Pages:: 1883–1893

Abstract

In graph theory, there are many quantitative values that are usually graph invariant and one such invariant that characterizes the structure or topology of a graph is called as topological index. Wiener index is one of the significant indices that quantifies the total of all shortest-path distances in the topology of a graph. After gaining recognition in the mid 20th century, its applications continue range across various fields including network theory, chemical graph theory, social network analysis and combinatorics. Here, we analyse and determine the Wiener index for the C6 C4 mesh topology-a combination of graphs constructed by interconnecting cycles of order 6 (C6) and order 4 (C4) in a mesh-like arrangement. We present unique formulas for the Wiener index of C6 C4 meshes, obtained from the wirelength of their respective embeddings.

Keywords

Embedding Wiener index Wirelength C6 C4 mesh topology

Subject Classifications

05C1205C3805C7605C8505C90

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