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Topological indices are molecular structural descriptors which computationally and theoretically describe the natures of the underlying connectivity of nanomaterials and chemical compounds, and hence they provide quicker methods to examine their activities and properties. Irregularity indices are mainly used to characterize the topological structures of irregular graphs. Graph irregularity studies are useful not only for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies, but also for predicting their various physical and chemical properties, including toxicity, resistance, melting and boiling points, the enthalpy of evaporation and entropy. In this article, we establish the expressions for the irregularity indices named as the variance of vertex degrees, σ irregularity index, and the discrepancy index of subdivision graph, vertex-semi total graph, edge-semi total graph, total graph, line graph, paraline graph, double graph, strong double graph and extended double cover of a graph.