A graph $G=(V,E)$ is $\gamma$-excellent if $V$ a union of all $\gamma$-sets $G$, where $\gamma$ stands for the domination number. Let $\mathcal{I}$ be set mutually nonisomorphic graphs and $\emptyset \not= \mathcal{H} \subsetneq \mathcal{I}$. In this paper we initiate study $\mathcal{H}$-$\gamma$-excellent graphs, which define as follows. $G$ following hold: (i) every $H \in \mathcal{H}$ each $...

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.