**ABSTRACT**

In this article, set valuations like set indexer, Topological set indexer, Topogenic set indexer, set graceful, set graceful were studied. The topological number and admissibility of Topogenic set indexers of certain graphs were determined. Also, the topological number of certain *T _{m,2}* graphs were computed. The relation between

*T*and

_{m,m}*T*and were established concerning specific bounds. Also, the Topological number of some merge graphs were analyzed.

_{2m-1,1}

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