Keywords and phrases: independent set, independent neighborhood system, graph polynomial.
Received: November 12, 2023; Revised: November 29, 2023; Accepted: December 20, 2023; Published: January 12, 2024
How to cite this article: Rosalio G. Artes Jr., Regimar A. Rasid, Sherna A. Rasid, Bayah J. Amiruddin-Rajik and Al-Jayson 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
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References:
[1] 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. [2] 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. [3] 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. [4] 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. [5] 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. [6] 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. [7] 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. [8] 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. [9] R. G. Artes Jr. and R. A. Rasid, Balanced biclique polynomial of graphs, Glob. J. Pure Appl. Math. 12(5) (2016), 4427-4433. [10] 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. [11] 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. [12] 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. [13] J. Ellis-Monaghan and J. Merino, Graph Polynomials and Their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011. [14] F. Harary, Graph Theory, CRC Press, Boca Raton, 2018. [15] 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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