Advances and Applications in Discrete Mathematics

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CONNECTED COMMON NEIGHBORHOOD SYSTEMS OF CLIQUES IN A GRAPH: A POLYNOMIAL REPRESENTATION

Authors

  • Amelia L. Arriesgado
  • Sonny C. Abdurasid
  • Rosalio G. Artes, Jr

Keywords:

clique, clique polynomial, clique common neighborhood polynomial, clique connected common neighborhood polynomial.

DOI:

https://doi.org/10.17654/0974165823019

Abstract

In 2022, Artes et al. [3] introduced a bivariate graph polynomial called the clique common neighborhood polynomial of a graph. In this paper, we extended the idea to connected common neighborhood system by restricting to the maximum connected subset of the common neighborhood system of a clique in a graph. Moreover, we establish the clique connected common neighborhood polynomials of complete bipartite graphs and complete q-partite graphs.

Received: February 7, 2023;
Accepted: March 11, 2023;

References

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.

R. Artes and L. Laja, Zeros of convex subgraph polynomials, Appl. Math. Sci. 8(59) (2014), 2917-2923.

R. Artes, M. Langamin and A. Calib-og, Clique common neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 35 (2022), 77-85.

J. Brown and R. Nowakowski, The neighborhood polynomial of a graph, Australas. J. Combin. 42 (2008), 55-68.

J. Ellis-Monaghan and J. Merino, Graph Polynomials and their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011.

I. Gutman, Graphs and graph polynomials of interest in chemistry, Gottfried Tinhofer and Gunther Schmidt, eds., Lecture Notes in Computer Science, Berlin, Springer-Verlag, 2005, pp. 177-187.

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.

U. S. R. Murty and J. A. Bondy, Graph Theory and Related Topics, Academic Press, New York, 1979.

J. Yellen and J. L. Gross, Graph Theory and its Applications, Chapman & Hall, New York, 2006.

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Published

2023-03-22

Issue

Vol. 38 No. 1 (2023)

Section

Articles

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Copyright (c) 2023 Pushpa Publishing House, Prayagraj, India

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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How to Cite

CONNECTED COMMON NEIGHBORHOOD SYSTEMS OF CLIQUES IN A GRAPH: A POLYNOMIAL REPRESENTATION. (2023). Advances and Applications in Discrete Mathematics, 38(1), 69-81. https://doi.org/10.17654/0974165823019

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