Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21285220201201New results on upper domatic number of graphs1251371399310.22049/cco.2019.26719.1136ENLibinSamuelCHRIST (Deemed to be University)0000-0002-0029-2408MAYAMMAJOSEPHCHRIST(Deemed to be University) Hosur Road
Bangalore-5600290000-0001-5819-247XJournal Article20191210For 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.http://comb-opt.azaruniv.ac.ir/article_13993_d2d2bdfc3ac890ae53ac04a1d2ad425e.pdf