On super $(a,d)-{P}_{2}\unicode{x22B3}H$ antimagic total labeling of disjoint union of comb product graphs

A Super $(a,d)-{P}_{2}\unicode{x22B3}H$ antimagic total labeling of a graph $G={C}_{n}\unicode{x22B3}H$ with $p=|V(G)|$ vertices and $q=|E(G)|$ edges is a bijective function λ from the set $\{V(G)\cup E(G)\}$ onto the set $\{1,2,3,\ldots |V(G)|+|E(G)|\}$ , such that the total ${P}_{2}\unicode{x22B3}H$ —weights, $\begin{array}{c}H\\ {w}_{{P}_{2}\unicode{x22B3}H}=\displaystyle {\sum }_{\upsilon \in V({P}_{2}\unicode{x22B3}H)}\lambda (\upsilon )+\displaystyle {\sum }_{e\in E({P}_{2}\unicode{x22B3}H)}\lambda (e)\end{array}$ , form an arithmetic sequence with the smallest label appears on the vertex. This paper discusses about super $(a,d)-{P}_{2}\unicode{x22B3}H$ antimagic total labeling of disjoint union of graph $G={C}_{n}\unicode{x22B3}H$ .