Common extremal graphs for three inequalities involving domination parameters
نویسندگان
1 University of Architecture, Civil Engineering and Geodesy (UACEG)
doi
10.22108/toc.2017.21464چکیده
Let $\delta (G)$, $\Delta (G)$ and $\gamma(G)$ be the minimum degree, maximum degree and domination number of a graph $G=(V(G), E(G))$, respectively. A partition of $V(G)$, all of whose classes are dominating sets in $G$, is called a domatic partition of $G$. The maximum number of classes of a domatic partition of $G$ is called the domatic number of $G$, denoted $d(G)$. It is well known that $d(G) \leq \delta(G) + 1$, $d(G)\gamma(G) \leq |V(G)|$ \cite{ch}, and $|V(G)| \leq (\Delta(G)+1)\gamma(G)$ \cite{berge}. In this paper, we investigate the graphs $G$ for which all the above inequalities become simultaneously equalities.
