Convex Independent Neighborhood Polynomial of Some Special Graphs

Authors

  • Edison John Aguilon Department of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines
  • Rosalio G. Artes Jr. Mathematics and Sciences Department, College of Arts and Sciences, Mindanao State University Tawi-Tawi College of Technology and Oceanography, Sanga-Sanga, 7500 Bongao, Philippines
  • Susan C. Dagondon Department of Mathematics and Statistics, College of Science and Mathematics, Center of Graph Theory, Algebra, and Analysis-Premier Research Institute of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5978

Keywords:

convex sets, convex subgraph, independent neighborhood system, independent set, convex independent neighborhood polynomial

Abstract

In this paper, we introduced the notion of convex independent neighborhood polynomial for a graph. We further explored the convex independent neighborhood polynomial for some special graphs such as paths, cycles, complete graphs, and star graphs. We generated these polynomials by counting the number of convex subsets of a graph with corresponding maximum independent set in the neighborhood system.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Discrete Mathematics

License

Copyright (c) 2025 Edison John Aguilon, Rosalio G. Artes Jr., Susan C. Dagondon

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How to Cite

Convex Independent Neighborhood Polynomial of Some Special Graphs. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5978. https://doi.org/10.29020/nybg.ejpam.v18i2.5978