Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

Submit Article

TRICLIQUE POLYNOMIALS AND TRICLIQUE NEIGHBORHOOD POLYNOMIALS OF SOME GRAPHS

Authors

  • Mohammad Nur S. Paspasan
  • Aldison M. Asdain
  • Eman C. Ahmad
  • Rosalio G. Artes Jr.

Keywords:

triclique, triclique polynomial, neighborhood system

DOI:

https://doi.org/10.17654/0974165825021

Abstract

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.

Published

2025-03-07

Issue

Section

Articles

How to Cite

TRICLIQUE POLYNOMIALS AND TRICLIQUE NEIGHBORHOOD POLYNOMIALS OF SOME GRAPHS. (2025). Advances and Applications in Discrete Mathematics, 42(4), 335-342. https://doi.org/10.17654/0974165825021

Similar Articles

1-10 of 62

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)