Total dominator color class total dominating sets in ladder and mobius ladder graph

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DOI:

https://doi.org/10.26637/MJM0901/0214

Abstract

Let $G$ be a finite, undirected and connected graph with minimum degree at least one. A proper coloring $\mathcal{C}$ of $G$ is said to be a total dominator color class total dominating set of $G$ if each vertex properly dominates a color class in $\mathcal{C}$ and each color class in $\mathcal{C}$ is properly dominated by a vertex in $\mathrm{V}(\mathrm{G})$. A total dominator color class total dominating set $D$ of $G$ is a minimal total dominator color class total dominating set if no proper subset of $D$ is a total dominator color class total dominating set of $G$. The total dominator color class total domination number is the minimum cardinality taken over all minimal total dominator color class total dominating sets in G and is denoted by $\gamma_{\chi}^{t d}(G)$. Here we obtain $\gamma_{\chi}^{t d}(G)$ for ladder graph and mobius ladder graph.

Keywords:

Chromatic number, Domination number, Total domination, Dominator color class dominating set, Total dominator color class total domination number

Mathematics Subject Classification:

05C15, 05C69
  • A. Vijayalekshmi Department of Mathematics, S.T.Hindu College, Nagercoil- 629002, Tamil Nadu, India. (Affiliated to Manonmaniam Sundaranar University, Tirunelveli- 627012)
  • S. Abisha Research Scholar, Reg.No: 20213152092019, Department of Mathematics, S.T.Hindu College, Nagercoil- 629002, Tamil Nadu, India. (Affiliated to Manonmaniam Sundaranar University, Tirunelveli- 627012)
  • Pages: 1233-1236
  • Date Published: 26-03-2021
  • Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

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Published

26-03-2021

How to Cite

A. Vijayalekshmi, and S. Abisha. “Total Dominator Color Class Total Dominating Sets in Ladder and Mobius Ladder Graph”. Malaya Journal of Matematik, vol. 9, no. 01, Mar. 2021, pp. 1233-6, doi:10.26637/MJM0901/0214.