Advances and Applications in Discrete Mathematics

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INDEPENDENT SETS IN THE NEIGHBORHOOD SYSTEMS OF BALANCED BICLIQUES: OPTIMIZATION AND POLYNOMIAL REPRESENTATIONS

Authors

  • Rosalio G. Artes Jr.
  • Regimar A. Rasid
  • Sherna A. Rasid
  • Bayah J. Amiruddin-Rajik
  • Al-Jayson U. Abubakar

Keywords:

balanced biclique, balanced biclique polynomial, balanced biclique independent neighborhood polynomial

DOI:

https://doi.org/10.17654/0974165824006

Abstract

In this paper, we determine the cardinality of an optimal independent set in the neighborhood system of a balanced biclique in a graph. We introduce a bivariate polynomial which represents the number of balanced bicliques corresponding to the cardinalities of maximum independent sets. Finally, we establish the explicit forms of the balanced biclique independent neighborhood polynomials of some special graphs.

Received: November 12, 2023
Revised: November 29, 2023
Accepted: December 20, 2023

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/10.17654/0974165823065.

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.

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

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Published

2024-01-12

Issue

Vol. 41 No. 1 (2024)

Section

Articles

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How to Cite

INDEPENDENT SETS IN THE NEIGHBORHOOD SYSTEMS OF BALANCED BICLIQUES: OPTIMIZATION AND POLYNOMIAL REPRESENTATIONS. (2024). Advances and Applications in Discrete Mathematics, 41(1), 97-104. https://doi.org/10.17654/0974165824006

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