  DNA graph has important contribution in completing the computational step of
DNA sequencing process. Using $(\alpha,k)$-labeling, several families of
digraphs have characterized as DNA graphs. Dicycles and dipaths are DNA graphs,
rooted trees and self adjoint digraphs are DNA graphs if and only if their
maximum degree is not greater than four, while the $m^{\text{th}}$ line digraph
of dicycle with one chord is a DNA graph for all $m\in\mathbb{Z}^+$. In this
paper we construct $(\alpha,k)$-labeling to show that for all
$m\in\mathbb{Z}^+$, the $m^{\text{th}}$ line digraph of dicycle $C_n$ with
$\left\lfloor{\frac{n}{3}}\right \rfloor$ chords are DNA graphs for $n\geq 6$,
and the $m^{\text{th}}$ line digraph of $\infty$-digraph $C_n\cdot C_p$ and
3-blade-propeller $C_n\cdot C_p \cdot C_q$ are DNA graphs for $n\geq 3$ and
certain values of $p$ and $q$.
