Keywords and phrases: convex set1, neighborhood system, convex neighborhood polynomial.
Received: June 29, 2023; Accepted: August 14, 2023; Published: August 25, 2023
How to cite this article: Sonny C. Abdurasid, Bayah J. Amiruddin, Jeffrey Imer C. Salim and Rosalio G. Artes Jr., Convex neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 40(1) (2023), 125-137. http://dx.doi.org/10.17654/0974165823061
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References: [1] N. Abdulcarim, S. Dagondon and E. Chacon, On the independent neighborhood polynomial of the Cartesian product of some special graphs, Eur. J. Pure Appl. Math. 14(1) (2021), 173-191. https://doi.org/10.29020/nybg.ejpam.v14i1.3860. [2] 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. [3] 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. [4] 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. [5] 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. [6] 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. [7] 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. [8] R. G. Artes Jr. and M. J. F. Luga, Convex accessibility in graphs, Appl. Math. Sci. 8(88) (2014), 4361-4366. http://dx.doi.org/10.12988/ams.2014.46467. [9] R. G. Artes Jr. and M. J. F. Luga, Convex accessibility in graph operations, Appl. Math. Sci. 8(116) (2014), 5763-5770. http://dx.doi.org/10.12988/ams.2014.47553. [10] 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. [11] 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. [12] 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. [13] R. G. Artes Jr. and R. A. Rasid, Balanced biclique polynomial of graphs, Glob. J. Pure Appl. Math. 12(5) (2016), 4427-4433. [14] 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. [15] J. I. Brown and R. J. Nowakowski, The neighbourhood polynomial of a graph, Australas. J. Combin. 42 (2008), 55-68. [16] J. Ellis-Monaghan and J. Merino, Graph Polynomials and their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011. [17] F. Harary, Graph Theory, CRC Press, Boca Raton, 2018. [18] C. Hoede and X. Li, Clique polynomials and independent set polynomials of graphs, Discrete Math. 125 (1994), 219-228. [19] 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. [20] 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. [21] 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. [22] 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. [23] 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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