Advances and Applications in Discrete Mathematics

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INDEPENDENT NEIGHBORHOOD POLYNOMIAL OF A GRAPH

Authors

  • Bayah J. Amiruddin-Rajik
  • Ruhilmina A. Sappayani
  • Rosalio G. Artes Jr.
  • Bhusra I. Junio
  • Hashirin H. Moh. Jiripa

Keywords:

independent set, neighborhood system, independent neighborhood polynomial.

DOI:

https://doi.org/10.17654/0974165824010

Abstract

In this paper, we introduce the concept of an independent neighborhood polynomial of a graph and obtain some of its properties. Moreover, we investigate the independent neighborhood polynomials of complete graphs, and complete bipartite graphs.

Received: December 3, 2023
Accepted: January 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.

R. G. Artes, Jr., N. H. R. Mohammad, A. A. Laja and N. H. M. Hassan, From graphs to polynomial rings: star polynomial representation of graphs, Advances and Applications in Discrete Mathematics 37 (2023), 67-76.

https://doi.org/10.17654/0974165823012.

R. G. Artes, Jr., N. H. R. Mohammad, Z. H. Dael and H. B. Copel, Star polynomial of the corona of graphs, Advances and Applications in Discrete Mathematics 39(1) (2023), 81-87. https://doi.org/10.17654/0974165823037.

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 neighborhoods systems, Advances and Applications in Discrete Mathematics 38(2) (2023), 179-189.

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

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.

C. Hoede and X. Li, Clique polynomials and independent set polynomials of graphs, Discrete Math. 125 (1994), 219-228.

R. E. Madalim, R. G. Eballe, A. H. Arajaini and R. G. Artes, Jr., Induced cycle polynomial of a graph, Advances and Applications in Discrete Mathematics 38(1) (2023), 83-94. https://doi.org/10.17654/0974165823020.

Rosalio G. Artes, Jr., Mercedita A. Langamin and Almira 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.

L. S. Laja and R. G. Artes Jr., Zeros of convex subgraph polynomials, Appl. Math. Sci. 8(59) (2014), 2917-2923. http://dx.doi.org/10.12988/ams.2014.44285.

L. S. Laja and R. G. Artes Jr., Convex subgraph polynomials of the join and the composition of graphs, International Journal of Mathematical Analysis 10(11) (2016), 515-529. http://dx.doi.org/10.12988/ijma.2016.512296.

C. A. Villarta, R. G. Eballe and R. G. Artes Jr., Induced path polynomial of graphs, Advances and Applications in Discrete Mathematics 39(2) (2023), 183-190. https://doi.org/10.17654/0974165823045.

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Published

2024-02-19

Issue

Vol. 41 No. 2 (2024)

Section

Articles

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Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

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How to Cite

INDEPENDENT NEIGHBORHOOD POLYNOMIAL OF A GRAPH. (2024). Advances and Applications in Discrete Mathematics, 41(2), 149-156. https://doi.org/10.17654/0974165824010

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