Comparative analysis of N-hydroxy-2,6-bis (p-chlorophenyl)-3-isopropylpiperidin-4-one semicarbazone and N-hydroxy-2,6-bis (p-chlorophenyl)-3-isopropylpiperidin-4-one thiosemicarbazone by graceful tree graph, non-graceful graph and cliques representation of graph with the data spectrum

In this paper, the graph theory has been developed into an extensive and popular branch of mathematics, which in turn has been applied to many problems in semicarbazone and thiosemicarbazone compounds. The compounds such as N-hydroxy-2,6-bis(pchlorophenyl)-3-isopropylpiperidin-4-one semicarbazone and N-hydroxy-2,6-bis(p-chlorophenyl)-3-isopropylpiperidin-4-one thiosemicarbazone have been synthesised and characterised on the basis of elemental analysis such as 1H NMR and 13C NMR. Several open problems that have gained respect with the help of graph theory, which can be recorded through simple, finite, connected and undirected group. The compounds which have been synthesised can be split into four sub groups. Each subset has been defined such as alkyl by graceful tree graph, N-hydroxy ring and phenyl compounds by non-graceful graph and semicarbazone and thiosemicarbazone by cliques representations of graph. The compound has been represented mathematically in terms of −p vertices and −q cliques. A complete picturisation of the compounds by combining all the subgroups together has been schematically icono-graphed.