Monophonic domination polynomial of the path graph

P. Arul Paul Sudhahar and W. Jebi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 4, Pages 787–796
DOI: 10.7546/nntdm.2024.30.4.787-796
Full paper (PDF, 222 Kb)

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Authors and affiliations

P. Arul Paul Sudhahar
Department of Mathematics, Government Arts and Science College
Nagercoil – 629004, Tamilnadu, India

W. Jebi
Department of Mathematics, Rani Anna Government College for Women
(Affiliated to Manonmaniam Sundaranar University)
Tirunelveli – 627008, Tamilnadu, India

Abstract

Let MD(G, i) be the family of monophonic dominating sets of a graph G with cardinality i and let \md(G, i) = |MD(G, i)|. Then the monophonic domination polynomial MD(G, x) of G is defined as MD(G, x) = \sum_{i = \gamma_m(G)}^{p} \md(G, i) x^i, where \gamma_m(G) is the monophonic domination number of G. In this paper we have determined the family of monophonic dominating sets of the path graph P_n with cardinality i. Also, the monophonic domination polynomial of the path graph is calculated and some properties of the coefficient \md(P_n, i) is discussed.

Keywords

  • Monophonic set
  • Monophonic dominating set
  • Monophonic domination polynomial
  • Path graph

2020 Mathematics Subject Classification

  • 05C12
  • 05C69

References

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Manuscript history

  • Received: 3 May 2023
  • Revised: 5 November 2024
  • Accepted: 21 November 2024
  • Online First: 23 November 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Arul Paul Sudhahar, P., & Jebi, W. (2024). Monophonic domination polynomial of the path graph. Notes on Number Theory and Discrete Mathematics, 30(4), 787-796, DOI: 10.7546/nntdm.2024.30.4.787-796.

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