@article {
author = {Samuel, Libin and Joseph, Mayamma},
title = {The upper domatic number of powers of graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {6},
number = {1},
pages = {53-65},
year = {2021},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2020.26913.1163},
abstract = {Let $A$ and $B$ be two disjoint subsets of the vertex set $V$ of a graph $G$. The set $A$ is said to dominate $B$, denoted by $A \rightarrow B$, if for every vertex $u \in B$ there exists a vertex $v \in A$ such that $uv \in E(G)$. For any graph $G$, a partition $\pi = \{V_1,$ $V_2,$ $\ldots,$ $V_p\}$ of the vertex set $V$ is an \textit{upper domatic partition} if $V_i \rightarrow V_j$ or $V_j \rightarrow V_i$ or both for every $V_i, V_j \in \pi$, whenever $i \neq j$. The \textit{upper domatic number} $D(G)$ is the maximum order of an upper domatic partition. In this paper, we study the upper domatic number of powers of graphs and examine the special case when power is $2$. We also show that the upper domatic number of $k^{\mathrm{th}}$ power of a graph can be viewed as its $ k$-upper domatic number.},
keywords = {Domatic number,$k$-domatic number,Upper domatic partition,Upper domatic number,$k$-upper domatic number},
url = {http://comb-opt.azaruniv.ac.ir/article_14108.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14108_7058eb1b6f8a087a8b1ec3b80f28c2ac.pdf}
}