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

BEHAVIOR OF BICLIQUE NEIGHBORHOOD POLYNOMIALS: 3D VISUALIZATION

Authors

  • Milagros C. Faustino
  • Regimar A. Rasid

Keywords:

biclique polynomial, neighborhood system, 3D visualization

DOI:

https://doi.org/10.17654/0974165824033

Abstract

Graph polynomials captured the interest of discrete mathematicians in recent years. The idea of graph polynomial is representing a graph structure by a polynomial capturing the number of substructures. The structure-neighborhood polynomial surfaced recently as a bivariate polynomial which clusters the structures with some specified neighborhood properties. In 2016, the balanced biclique polynomial was introduced. Recently, the balanced biclique independent neighborhood polynomials have been investigated for several graphs. In this paper, we investigate the behavior of the 3D plot of cycle graph polynomial representations for varying orders of the structure. Moreover, we investigate the balanced biclique independent neighborhood polynomial of stars and visualize the graph polynomials in 3D.

Received: June 16, 2024
Accepted: July 27, 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, International Journal of Mathematics and Computer Science 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, Global Journal of Pure and Applied Mathematics 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.

R. G. Artes Jr., R. A. Rasid, S. A. Rasid, B. J. Amiruddin-Rajik and A. J. U. Abubakar, Independent sets in the neighborhood systems of balanced bicliques: Optimization and polynomial representations, Advances and Applications in Discrete Mathematics 41(1) (2024), 97-104.

http://dx.doi.org/10.17654/0974165824006

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

2024-08-09

Issue

Vol. 41 No. 6 (2024)

Section

Articles

License

Copyright (c) 2024 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

BEHAVIOR OF BICLIQUE NEIGHBORHOOD POLYNOMIALS: 3D VISUALIZATION. (2024). Advances and Applications in Discrete Mathematics, 41(6), 493-503. https://doi.org/10.17654/0974165824033

Similar Articles

1-10 of 62

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

Most read articles by the same author(s)