Department of Chemistry, Durgapur Government College, J. N. Avenue, Durgapur-713 214, West Bengal, India E-mail: bankimghosh@yahoo.co.in Manuscript received online 09 November 2019, accepted 18 November 2019 Fullerene structures can be built up step by step by adding C2 -fragments to pentagons and hexagons of sp2 -carbon atoms systematically; if in this building process fusion of pentagons are avoided and the Euler formula is obeyed, structures of carbon cages corresponding to the IPR fullerenes are obtained. Graph theoretical method involving 5- and 6-fold rotational symmetry can be used to obtain the 𝝅-MO energies of the sub-structures and also of the complete cage structure. This has been done in the present work and it has been shown that the total 𝝅-electron energy per atom gradually decreases as the substructures grow with addition of C2 -fragments and in the last step when the cage closure is complete, the stabilization is very much appreciable. The method has been shown with the IPR fullerenes C60, C70, C72 and C84.