Some invariants related to threshold and chain graphs

Let $ G = (V, E) be a finite simple connected graph. We say graph realizes code of the type 0^{s_1}1^{t_1}0^{s_2}1^{t_2}\cdots0^{s_k}1^{t_k} if and only can obtained from by some rule. Some classes graphs such as threshold chain mentioned above. The main objective this research article is to develop computationally feasible methods determine interesting theoretical invariants. present an efficient algorithm metric dimension graphs. compute restricted discuss L(2, 1) $-coloring in In fact, for every $, we establish formula which obtain \lambda $-chromatic number $. Finally, provide