The use of discrete mathematics in chemistry to model the physical and biological aspects of chemical substances is known as chemical graph theory. The chemical applications of graph theory are used to determine a wide range of parameters, including physio-chemical properties, thermodynamic properties, chemical activity, and biological activity. A topological index, which is regarded as a structural invariant, is a real number associated with a graph. It has been discovered that there is a significant relationship between the topological indices of chemical compounds and their properties. The symmetry of irregular shape graphs can be treated by irregularity indices, in better way. In this paper, we will investigate the molecular graphs of Fractal tree and Cayley tree dendrimer with the help of ten famous irregularity indices.