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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COMBINATORIAL APPROACH FOR COUNTING GEODETIC SETS WITH SUBDOMINATING NEIGHBORHOOD SYSTEMS

Authors

  • Rosalio G. Artes, Jr
  • Josephine B. Nalzaro

Keywords:

geodetic set, dominating set, neighborhood system, geodetic subdominating neighborhood polynomial.

DOI:

https://doi.org/10.17654/0974165823027

Abstract

In this paper, we introduce the concept of geodetic subdominating neighborhood polynomials of a graph and determine the geodetic subdominating neighborhood polynomials of a complete bipartite graph and that of a complete $q$-partite graph.

Received: January 18, 2023;
Accepted: March 30, 2023;

References

S. Alikhani and Y. Peng, Introduction to domination polynomial of a graph, Ars. Combin. 114 (2014), 257-266.

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.

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, Springer-Verlag, Berlin, 2005, pp. 177-187.

F. Harary, Graph Theory, CRC Press, Boca Raton, 2018.

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.

A. Vijayan and K. Vijila Dafini, On geodetic sets and geodetic polynomials of wheels and paths, Int. J. Math. Sci. Eng. Appl. 6(3) (2012), 123-137.

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Published

2023-04-18

Issue

Vol. 38 No. 2 (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

COMBINATORIAL APPROACH FOR COUNTING GEODETIC SETS WITH SUBDOMINATING NEIGHBORHOOD SYSTEMS. (2023). Advances and Applications in Discrete Mathematics, 38(2), 179-189. https://doi.org/10.17654/0974165823027

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