%0 Journal Article
%T New results on upper domatic number of graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Samuel, Libin
%A JOSEPH, MAYAMMA
%D 2020
%\ 12/01/2020
%V 5
%N 2
%P 125-137
%! New results on upper domatic number of graphs
%K domination
%K Upper domatic partition
%K Upper domatic number
%K Transitivity
%R 10.22049/cco.2019.26719.1136
%X For a graph $G = (V, E)$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_k}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ 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. We study the properties of upper domatic number and propose an upper bound in terms of clique number. Further, we discuss the upper domatic number of certain graph classes including unicyclic graphs and power graphs of paths and cycles.
%U http://comb-opt.azaruniv.ac.ir/article_13993_d2d2bdfc3ac890ae53ac04a1d2ad425e.pdf