Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

Submit Article

INDEPENDENT VERTEX NEIGHBORHOOD POLYNOMIALS: BEHAVIOR OF GRAPHS AND SOME APPLICATIONS

Authors

  • Zuraida J. Bara
  • Regimar A. Rasid
  • Rosalio G. Artes Jr.

Keywords:

independent vertex neighborhood, graph polynomial

DOI:

https://doi.org/10.17654/0974165825003

Abstract

In this paper, we established the independent vertex neighborhood polynomials of complete graphs, paths, cycles, and complete bipartite graphs. In addition, we investigated these polynomials in terms of intersection points in the plane. Visual representations of graphs are presented to have closer properties of the polynomials comparing for different values of the order of the graph. Moreover, we model a social network activity as an application of this polynomial representation.

Received: September 29, 2024
Accepted: November 16, 2024

References

R. A. Anunciado and R. G. Artes Jr., Connected dominating independent neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 39(1) (2023), 73-80. https://doi.org/10.17654/0974165823036.

A. L. Arriesgado and R. G. Artes Jr., Convex independent common neighborhood polynomial of a graph, Advances and Applications in Discrete Mathematics 38(2) (2023), 145-158. https://doi.org/10.17654/0974165823025.

A. L. Arriesgado, S. C. Abdurasid and R. G. Artes Jr., Connected common neighborhood systems of cliques in a graph: a polynomial representation, Advances and Applications in Discrete Mathematics 38(1) (2023), 69-81. https://doi.org/10.17654/0974165823019.

A. L. Arriesgado, J. I. C. Salim and R. G. Artes Jr., Clique connected common neighborhood polynomial of the join of graphs, Int. J. Math. Comput. Sci. 18(4) (2023), 655-659.

A. L. Arriesgado, J. I. C. Salim and R. G. Artes Jr., Polynomial representation of the neighborhood systems of cliques in the corona of graphs, Advances and Applications in Discrete Mathematics 40(1) (2023), 11-18.

https://doi.org/10.17654/0974165823054

R. G. Artes Jr., A. J. U. Abubakar and S. U. Kamdon, Polynomial representations of the biclique neighborhood of graphs, Advances and Applications in Discrete Mathematics 37 (2023), 37-45. http://dx.doi.org/10.17654/0974165823010.

R. G. Artes Jr., R. H. Moh. Jiripa and J. I. C. Salim, Connected total dominating neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 39(2) (2023), 145-154. http://dx.doi.org/10.17654/0974165823042.

R. G. Artes Jr. and J. B. Nalzaro, Combinatorial approach for counting geodetic sets with subdominating neighborhood systems, Advances and Applications in Discrete Mathematics 38(2) (2023), 179-189.

https://doi.org/10.17654/0974165823027.

R. G. Artes Jr. and R. A. Rasid, Balanced biclique polynomial of graphs, Glob. J. Pure Appl. Math. 12(5) (2016), 4427-4433.

R. G. Artes Jr. and R. A. Rasid, Combinatorial approach in counting the balanced bicliques in the join and corona of graphs, Journal of Ultra Scientist of Physical Sciences 29(5) (2017), 192-195.

A. M. Asdain, B. J. Amiruddin, R. A. Rasid, J. I. C. Salim and R. G. Artes Jr., Polynomial representations of a balanced biclique common neighborhood system of graphs, Advances and Applications in Discrete Mathematics 40(2) (2023), 187-194. https://doi.org/10.17654/097416582306.

A. R. Bakkang, R. A. Rasid and R. G. Artes Jr., Combinatorial approach in counting the neighbors of cliques in a graph, Advances and Applications in Discrete Mathematics 40(2) (2023), 167-175.

https://doi.org/10.17654/0974165823063.

J. Ellis-Monaghan and J. Merino, Graph Polynomials and their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011.

F. Harary, Graph Theory, CRC Press, Boca Raton, 2018.

M. A. Langamin, A. B. Calib-og and R. G. Artes Jr., Clique common neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 35 (2022), 77-85. https://doi.org/10.17654/0974165822053.

Downloads

Published

2024-11-19

Issue

Vol. 42 No. 1 (2025)

Section

Articles

License

Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

Creative Commons License

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

_________________________

Licensing Terms:

Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.

Contact Pushpa Publishing House for more info or permissions.

How to Cite

INDEPENDENT VERTEX NEIGHBORHOOD POLYNOMIALS: BEHAVIOR OF GRAPHS AND SOME APPLICATIONS. (2024). Advances and Applications in Discrete Mathematics, 42(1), 47-54. https://doi.org/10.17654/0974165825003

Similar Articles

1-10 of 160

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)

1 2 > >>