A new approach for synthesis of N-hydroxy-2, 6–bis (p-hydroxyphenyl)-3 isopropyl piperdin-4-onethiosemicarbazone has been developed from the Graph theory. A key step to access the characterization of the synthesized compound was achieved, by the elemental analysis IR, 1H NMR and 13C NMR and Raman spectral data. This Graph theory has developed a great target of interest for synthetic organic chemistry because of its structural simplicity, efficient methods and convenient roots are still being sought after. This strategy involves the in situ classification of Graph theory and further it has been discussed mathematically in terms of p – vertices and q – cliques. In order to illustrate the efficiency of our method, we are interested in extending this methodology to privileged structures of Graph theory. The good functional group compatibility renders the synthesized compound into four sub groups. Each subset of a group has been defined, such as dialkyl by complete Tripartite Graph, thiosemicarbazone by Complete Bipartite Graph, N-hydroxy ring and halo aromatic compounds are represented by Complete Split Graph analysis. This work has been taken up with an idea of a complete picturization of the compound by combining all the subgroups together and it also been schematically represented.