Bounds of Geodetic-Wiener Index on Spirocyclic Graphs

Authors

  • Rosalio Artes Jr. Department of Mathematics, College of Arts and Sciences, Mindanao State University - Tawi-Tawi College of Technology and Oceanography, 7500 Bongao, Tawi-Tawi, Philippines
  • Rudrusamy Gobithaasan School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia
  • Roslan Hasni Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, 21030 UMT Kuala Nerus, Terengganu, Malaysia
  • Nader Jafari Rad Department of Mathematics, Shahed University, Tehran, Iran

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6212

Keywords:

Topological index, Geodetic-Wiener index, Spirocyclic graphs

Abstract

Wiener index has been extensively studied for several decades because of its applications in chemistry. Many variants of Wiener index were defined and their corresponding bounds were explored. In this work, we introduced the concept of geodetic-Wiener index by considering the number of geodesics between any pair of vertices. We used the concept of projection of a vertex to a subgraph to decompose the structure into subtrees. Simple spirocyclic graphs are bicyclic graphs whose cycles share a common vertex. Using the idea of partial Wiener index, we determined the bounds of geodetic-Wiener index with respect to other distance-based topological indices for simple spirocyclic graphs. 

Downloads

Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Discrete Mathematics

License

Copyright (c) 2025 Rosalio Artes Jr., Rudrusamy Gobithaasan, Roslan Hasni, Nader Jafari Rad

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Bounds of Geodetic-Wiener Index on Spirocyclic Graphs. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6212. https://doi.org/10.29020/nybg.ejpam.v18i4.6212