Double total domination number in certain chemical graphs

Let $G$ be a graph with the vertex set $V(G)$. A set $D\subseteq V(G)$ is a total k-dominating set if every vertex $v\in V(G)$ has at least $k$ neighbours in $D$. The total k-domination number ${\gamma }_{kt}(G)$ is the cardinality of the smallest total k-dominating set. For $k=2$ the total 2-dominating set is called double total dominating set. In this paper we determine the upper and lower bounds and some exact values for double total domination number on pyrene network $PY(n)$, $n\ge 1$ and hexabenzocoronene $XC(n)$ $n\ge 2$, where pyrene network and hexabenzocoronene are composed of congruent hexagons.