TRICLIQUE POLYNOMIALS AND TRICLIQUE NEIGHBORHOOD POLYNOMIALS OF SOME GRAPHS
Keywords:
triclique, triclique polynomial, neighborhood systemDOI:
https://doi.org/10.17654/0974165825021Abstract
In this paper, we introduce the concept of balanced triclique polynomial and balanced triclique neighborhood polynomial of graphs. First, we characterize the balanced tricliques in complete graphs of order at least three and complete $q$-particle graphs for $q \geq 3.$ Moreover, we establish the corresponding polynomials.
Received: October 16, 2024
Revised: December 17, 2024
Accepted: January 21, 2025
References
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.
http://dx.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 Journals of Mathematics and Computer Science 18(4) (2023), 655-659.
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.
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., 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. 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., J. I. C. Salim, R. A. Rasid, J. I. Edubos and B. J. Amiruddin, Geodetic closure polynomial of graphs, Int. J. Math. Comput. Sci. 19(2) (2024), 439-443.
J. I. Brown and R. J. Nowakowski, The Neighbourhood polynomial of a graph, Australian Journal of Combinatorics 42 (2008), 55-68.
J. Ellis-Monaghan and J. Merino, Graph Polynomials and their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011.
E. Farrel, A note on the clique polynomial and its relation to other graph polynomials, Journal of Mathematical Science 8 (1997), 97-102.
F. Harary, Graph Theory, CFC Press, Boca Raton, 1969.
C. Hoede and X. Li, Clique polynomials and independent set polynomials of graphs, Discrete Mathematics 125 (1994), 219-228.
S. M. B. Lumpayao, R. A. Rasid and R. G. Artes Jr., On biclique polynomials, Advances and Applications in Discrete Mathematics 41(3) (2024), 231-237.
http://dx.doi.org/10.17654/0974165824017.
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.
J. F. B. Maldo and R. G. Artes Jr., Applications of Chuh-Shih-Chieh’s identity in geodetic independence polynomials, International Journal of Mathematics and Computer Science 19(3) (2024), 649-652.
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.
C. A. Villarta, R. G. Eballe and R. G. Artes Jr., Induced path polynomials of the join and corona of graphs, Int. J. Math. Comput. Sci. 19(3) (2024), 643-647.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
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.
Journal Impact Factor: 