Pendant Total Domination Polynomial of Some Families of Standard Graphs

Authors

DOI:

https://doi.org/10.26713/cma.v14i2.2193

Keywords:

Dominating Set (DS), Total Dominating Set (TDS), Pendant Total Domination (PTD), Pendant Total Dominating Set (PTDS), Pendant Total Domination Number (PTDN)

Abstract

In this article, our aim is to determine the pendant total domination polynomial of some families of standard graphs and obtain some properties of coefficients and nullity of the pendant total domination polynomial of a connected graph \(\mathcal{G}\). Consider \(\mathcal{G}\) as a simple connected graph and its vertex and edge sets are defined as \(\mathcal{V}_\calG\) and \(\mathcal{E}_\calG\), respectively. A set \(\mathcal{T} \subseteq \mathcal{V}_\calG\) is said to be a total dominating set of graph \(\mathcal{G}\) if all the vertices of the graph must attached with some vertex of \(\mathcal{T} \). A set \(\mathcal{T} \subseteq \mathcal{V}_\calG\) is said to be a PTDS if \(\mathcal{T}\) is a TDS and \(\langle \mathcal{T} \rangle\) contains at least a single pendant vertex.

Downloads

Download data is not yet available.

References

S. Alikhani, On the domination polynomial of some graph operations, International Scholarly Research Notices 2013 (2013), Article ID 146595, 3 pages, DOI: 10.1155/2013/146595.

S. Alikhani and Y. H. Peng, Introduction to Domination Polynomial of a Graph, Ars Combinatoria 114(2014), 257 – 266, URL: http://combinatoire.ca/ArsCombinatoria/ACgetit.php?vol=114&paper=26.

J. L. Arocha and B. Llano, Mean value for the matching and dominating polynomial, Discussiones Mathematicae Graph Theory 20(1) (2000), 57 – 69, DOI: 10.7151/dmgt.1106.

B. Chaluvaraju and V. Chaitra, Total domination polynomial of a graph, Journal of Informatics and Mathematical Sciences 6(2) (2014), 87 – 92, DOI: 10.26713/jims.v6i2.256.

E. J. Cockayne, R. M. Dawes and S. T. Hedetniemi, Total domination in graphs, Networks 10(3) (1980), 211 – 219, DOI: 10.1002/net.3230100304.

I. Gutman and B. Borovicanin, Nullity of graphs: An updated survey, Zbornik Radova 22 (2011), 137 – 154, URL: http://elib.mi.sanu.ac.rs/files/journals/zr/22/zbr14137.pdf.

S. R. Nayaka, Puttaswamy and S. Purushothama, Pendant domination in graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 112(1) (2020), 219 – 230.

S. R. Nayaka, Puttaswamy and S. Purushothama, Pendant domination polynomial of a graph, International Journal of Pure and Applied Mathematics 117(11) (2017), 193 – 199, URL: https://acadpubl.eu/jsi/2017-117-11-14/articles/11/23.pdf.

J. Rani and S. Mehra, Pendant total domination number of some generalized graphs, Advances and Applications in Discrete Mathematics 33 (2022), 19 – 44, DOI: 10.17654/0974165822036.

Downloads

Published

18-09-2023
CITATION

How to Cite

Rani, J., & Mehra, S. (2023). Pendant Total Domination Polynomial of Some Families of Standard Graphs. Communications in Mathematics and Applications, 14(2), 647–654. https://doi.org/10.26713/cma.v14i2.2193

Issue

Vol. 14 No. 2 (2023)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.