In this work N-hydroxy-3,5– dimethyl–2,6–diphenylpiperdin-4-one–semicarbazone has been synthesized and it has been characterized on the basis of elemental analysis IR, 1H NMR, 13C NMR and Raman spectral data. Several complex compounds can be easily picturized with the help of graph theory, which can be recorded through simple, finite, connected and undirected graph. The compound which has been synthesized can be split into four sub groups .Each subset has been defined, such as semicarbazone by Complete Bipartite Graph, alkyl by Tree Graph and Nhydroxy ring and phenyl compound by Complete Split Graph. This representation has been discussed mathematically in terms of p – vertices and q – cliques. A complete picturization of the compound by combining all the sub groups together has also been schematically icono-graphed.