The molecular topological indices as validly demonstrated its high performance in the discovery and design of new drugs. The goal of this paper is to study the structurally constructed a graph model of human Liver using graph operator. After the construction, nurtured the model using various topological indices. Also, established a diagnosis defect in the human Liver. Basically, considered structure of Liver can divide into healthy Liver and affected Liver. In this case study the topological indices are used in describe the structure of Liver using graph operator. Constructed model can be useful further in the medical field for any diagnosis with special care.