Weighted Szeged indices of some graph operations

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.