© 2020 Elsevier Inc.In this study, we investigated and revealed the electronic properties, geometric structures and binding behavior of small (IrO)n and (IrO2)n (n = 1–5) clusters within first principles calculations based on the density functional theory. The electronic and magnetic properties of small nanoclusters displayed significant size dependency due to strong quantum confinement effect. Moreover we considered the binding and structural modification of the clusters on graphene surface as a substrate. The cohesive energy per atom of isolated clusters increased with size of the cluster n. This shows that the increase in coordination number results in a more stable nanocluster with increased number of saturated bonds. Pristine (IrO)n and (IrO2)n clusters presented different structural motives at equilibrium. The ground states of (IrO)n and (IrO2)n clusters considered in this study were all magnetic except for (IrO)4, (IrO2)2, and (IrO2)4. HOMO-LUMO gap EHLG values displayed large variations due to size of the cluster, hence bond saturation. The structural configurations of free standing nanoclusters are slightly modified, when adsorbed on graphene. The adsorption behavior of a cluster on graphene was improved by an applied electric field yielding larger binding energy and larger charger transfer. We observed that electronic and magnetic ground state of the clusters strongly depend on optimized structural configuration for both bare and adsorbed on graphene monolayer.