In this paper, the weighted Szeged indices of Cartesian product and Corona product of two connected graphs are obtained. Using the results obtained here, the weighted Szeged indices of the hypercube of dimension $n$, Hamming graph, $C_4$ nanotubes, nanotorus, grid, $t-$fold bristled, sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

1] R. Balakrishnan and K. Ranganathan, A Text Book of Graph Theory, Springer-Verlag, New York, 2000.

[2] A. A. Dobrynin, I. Gutman and G. Domotor, A Wiener-type graph invariant for some bipartite graphs, Appl. Math. Lett., 8 (1995) 57-62.

[3] I. Gutman, P. V. Khadikar, P. V. Rajput and S. Karmarkar, The Szeged index of polyacenes, J. Serb. Chem. Soc., 60 (1995) 759-764.

[4] I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N. Y., 27 (1994) 9-15.

[5] I. Gutman and A. A. Dobrynin, The Szeged index-a success story, Graph Theory Notes N. Y., 34 (1998) 37{44.

[6] W. Imrich and S. Klavzar, Product graphs: Structure and Recognition, John Wiley, New York, 2000.

[7] M. H. Khalifeh, H. Youse-Azari, A. R. Ashra and I. Gutman, The edge Szeged index of product graphs, Croatica Chemica Acta, 81 (2008) 277-281.

[8] S. Klavzar, A. Ra japakse and I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett., 9 (1996) 45-49.

[9] P. V. Khadikar, N. V. Deshpande, P. P. Kale, A. A. Dobrynin and I. Gutman, The Szeged index and an analogy with the Wiener index, J. Chem. Inf. Comput. Sci., 35 (1995) 547-550.

[10] M. J. Nadja-Arani, H. Kho dashenas and A. R. Ashra, On the diﬀerences between Szeged and Wiener indices of graphs, Discrete Math., 311 (2011) 2233 {2237.

[11] A. Ilic and N. Milosavljevic, The Weighted vertex PI index, Math. Comput. Model ling, 57 (2013) 623-631.

[12] Z. Yarahmadi and A. R. Ashra, The Szeged, vertex PI, rst and second Zagreb indices of corona product of graphs, Filomat, 26 (2012) 467-472.

[13] M. Alaeiyan, J. Asadp our and R. Mo jarad, Computing of some top ological indices of corona product graphs, Australian J. Basic Appl. Sci., 5 (2011) 145-152.

[14] M. Tavakoli and H. Youse-Azari, Computing PI and hyp er-Wiener indices of corona product of some graphs, Iranian J. Math. Chem., 1 (2010) 131-135.

[15] I. Gutman, B. Ruscic, N. Trina jstic and C. F. Wilcox, Graph theory and molecular orbitals.XII. Acyclicpolyenes, J. Chem. Phys., 62 (1975) 3399-3405.

[16] I. Gutman and N. Trina jstic, Graph theory and molecular orbitals. Total Φ-electron energy of alternant hydro car-bons, Chem.Phys. Lett., 17 (1972) 535-538.

[17] K. Pattabiraman and P. Kandan, Weighted PI indices of some graph operations, to appear in Electronic Notes in Discrete Mathematics.

[18] T. Pisanski and M. Randic, Use of the Szeged index and the revised Szeged index for measuring network bipartivity, Discrete Appl. Math., 158 (2010) 1936-1944.

[19] M. Randic, M. Novic and D. Plavsic, Common vertex matrix: A novel characterization of molecular graphs by counting, J. Comput. Chem., 34 (2013) 1409-1419.

[20] A. Milicevic and N. Trina jstic, Combinatorial enumeration in chemistry, in:A. Hincliffe (Ed.), chemical modelling: Application and Theory, 4, RSC Publishing, Cambridge, 2006 405-469.