Total dominator color class total dominating sets in ladder and mobius ladder graph
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DOI:
https://doi.org/10.26637/MJM0901/0214Abstract
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 numberMathematics Subject Classification:
05C15, 05C69- Pages: 1233-1236
- Date Published: 26-03-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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