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arXiv · 1801.06500

Total dominator chromatic number of $k$-subdivision of graphs

Saeid Alikhani·Nima Ghanbari·Samaneh Soltani
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Abstract

Let $G$ be a simple graph. A total dominator coloring of $G$, is a proper coloring of the vertices of $G$ in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic (TDC) number $\chi_d^t(G)$ of $G$, is the minimum number of colors among all total dominator coloring of $G$. For any $k \in \mathbb{N}$, the $k$-subdivision of $G$ is a simple graph $G^{\frac{1}{k}}$ which is constructed by replacing each edge of $G$ with a path of length $k$. In this paper, we study the total dominator chromatic number of $k$-subdivision of $G$.

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Saeid Alikhani, Nima Ghanbari, Samaneh Soltani. 2018-01-19. Total dominator chromatic number of $k$-subdivision of graphs. https://arxiv.org/abs/1801.06500

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