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.

Submit Article

PENDANT TOTAL DOMINATION NUMBER OF SOME GENERALIZED GRAPHS

Authors

  • Jyoti Rani
  • Seema Mehra

Keywords:

DS, TDS, PTDS, PTDN

DOI:

https://doi.org/10.17654/0974165822036

Abstract

For a given graph $\mathcal{G}=(\mathcal{V}, \mathcal{E})$, a total dominating set $\mathcal{T}$ is called a pendant total dominating set if the subgraph $\langle\mathcal{T}\rangle$ induced by $\mathcal{T}$ contains at least one pendant vertex. The cardinality of a pendant total dominating set with smallest cardinal number is known as pendant total domination number of $\mathcal{G}$. In this paper, we determine the pendant total domination number of some generalized graphs.

Received: May 6, 2022
Accepted: July 15, 2022

References

E. J. Cockayne, R. M. Dawes and S. T. Hedetniemi, Total domination in graphs, Networks 10 (1980), 211-219.

J. Rani and S. Mehra, Pendant total domination in graphs, Advances and Applications in Mathematical Sciences (in communication).

M. A. Henning and A. Yeo, Total domination in graphs, Springer Monographs in Mathematics, New York, 2013.

S. R. Nayaka, Puttaswamy and S. Purushothama, Pendant domination in graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 112(1) (2020), 219-229.

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs Advanced Topics, Marcel Dekker, New York, 1998.

Downloads

Published

2022-08-03

Issue

Vol. 33 (2022)

Section

Articles

License

Copyright (c) 2022 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

Creative Commons License

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

_________________________

Licensing Terms:

Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.

Contact Pushpa Publishing House for more info or permissions.

How to Cite

PENDANT TOTAL DOMINATION NUMBER OF SOME GENERALIZED GRAPHS. (2022). Advances and Applications in Discrete Mathematics, 33, 19-44. https://doi.org/10.17654/0974165822036