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.

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POLYNOMIAL REPRESENTATIONS OF A BALANCED BICLIQUE COMMON NEIGHBORHOOD SYSTEM OF GRAPHS

Authors

  • Aldison M. Asdain
  • Bayah J. Amiruddin
  • Regimar A. Rasid
  • Jeffrey Imer C. Salim
  • Rosalio G. Artes Jr.

Keywords:

balanced biclique, balanced biclique polynomial, balanced biclique common neighborhood polynomial.

DOI:

https://doi.org/10.17654/0974165823065

Abstract

A biclique in a graph $G$ is a subset of $V(G)$ which induces a complete bipartite subgraph of $G$. It is said to be balanced if it has equivalent independent vertex partitions. In this paper, we introduce a graph polynomial which represents the number of balanced bicliques of $G$ of all possible orders with corresponding common neighborhood systems and establish some results on some special graphs.

Received: September 25, 2023
Revised: October 10, 2023
Accepted: November 1, 2023

References

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.

R. G. Artes, Jr. and R. A. Rasid, Balanced biclique polynomial of graphs, Glob. J. Pure Appl. Math. 12(5) (2016), 4427-4433.

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. 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.

J. A. Ellis-Monaghan and C. Merino, Graph polynomials and their applications II: interrelations and interpretations, Structural Analysis of Complex Networks, M. Dehmer, ed., Birkhauser Boston, 2011.

I. Gutman, Graphs and graph polynomials of interest in chemistry, applications in chemistry, Lecture Notes in Computer Science Series (LNCS), Volume 246, 2005.

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Published

2023-11-04

Issue

Vol. 40 No. 2 (2023)

Section

Articles

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How to Cite

POLYNOMIAL REPRESENTATIONS OF A BALANCED BICLIQUE COMMON NEIGHBORHOOD SYSTEM OF GRAPHS. (2023). Advances and Applications in Discrete Mathematics, 40(2), 187-194. https://doi.org/10.17654/0974165823065

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