References

  1. Gutman I., Trinajstić N. Graph theory and molecular orbitals. Total $\phi$-electron energy of alternant hydrocarbons. Chemical Physics Letters 1972, 17 (4), 535-538. doi: 10.1016/0009-2614(72)85099-1
  2. Xu K., Tang K., Liu H., Wang J. The Zagreb indices of bipartite graphs with more edges. J. Appl. Math. Inf. 2015, 33 (3-4), 365-377. doi: 10.14317/jami.2015.365
  3. Das K.C., Xu K., Nam J. Zagreb indices of graphs. Front. Math. China 2015, 10 (3), 567-582. doi: 10.1007/s11464-015-0431-9
  4. Zhou B. Upper bounds for the Zagreb indices and the spectral radius of series-parallel graphs. Int. J. Quantum Chem. 2007, 107 (4), 875-878. doi: 10.1002/qua.21223
  5. Zhou B., Gutman I. Further properties of Zagreb indices. MATCH Commun. Math. Comput. Chem. 2005, 54, 233-239.
  6. Tavakoli M., Rahbarnia F., Ashrafi A.R. Eccentric connectivity and Zagreb coindices of the generalized hierarchical product of graphs. J. Discrete Math. 2014, 2014, article id 292679. doi: 10.1155/2014/292679
  7. Khalifeha M.H., Yousefi-Azaria H., Ashrafi A.R. The first and second Zagreb indices of some graph operations. Discrete Appl. Math. 2009, 157 (4), 804-811. doi: 10.1016/j.dam.2008.06.015
  8. Ashrafi A.R., Doslić T., Hamzeh A. The Zagreb coindices of graph operations. Discrete Appl. Math. 2010, 158 (15), 1571-1578. doi: 10.1016/j.dam.2010.05.017
  9. Das K.C., Yurttas A., Togan M., Cevik A.S., Cangul I.N. The multiplicative Zagreb indices of graph operations. J. Inequal. Appl. 2013, 2013:90. doi: 10.1186/1029-242X-2013-90
  10. De N., Nayeem S.M.A., Pal A. F-index of some graph operations. Discrete Math. Algorithm. Appl. 2016, 8 (2), article id 1650025. doi: 10.1142/S1793830916500257
  11. De N., Nayeem S.M.A., Pal A. The F-coindex of some graph operations. SpringerPlus 2016, 5 (221). doi: 10.1186/s40064-016-1864-7
  12. De N., Nayeem S.M.A. Pal A. Reformulated Zagreb index of some graph operations. Mathematics 2015, 3 (4), 945-960. doi: 10.3390/math3040945
  13. Azari M., Iranmanesh A. Computing the eccentric-distance sum for graph operations. Discrete Appl. Math. 2013, 161 (18), 2827-2840. doi: 10.1016/j.dam.2013.06.003
  14. De N., Pal A., Nayeem S.M.A. Modified eccentric connectivity of generalized thorn graphs. Int. J. Comput. Math. 2014, 2014, article id 436140. doi: 10.1155/2014/436140
  15. Azari M. Sharp lower bounds on the Narumi-Katayama index of graph operations. Appl. Math. Comput. 2014, 239, 409-421. doi: 10.1016/j.amc.2014.04.088
  16. Azari M., Iranmanesh A. Some inequalities for the multiplicative sum Zagreb index of graph operations. J. Math. Ineql. 2015, 9 (3), 727-738. doi: 10.7153/jmi-09-60
  17. De N., Pal A., Nayeem S.M.A. The irregularity of some composite graphs. Int. J. Appl. Comput. Math. 2016, 2 (3), 411-420. doi: 10.1007/s40819-015-0069-z
  18. De N., Pal A., Nayeem S.M.A. On some bounds and exact formulae for connective eccentric indices of graphs under some graph operations. Int. J. Comb. 2014, 2014, article id 579257. doi: 10.1155/2014/579257
  19. Khalifeh M.H., Yousefi-Azari H., Ashrafi A.R. The hyper-Wiener index of graph operations. Comput. Math. Appl. 2008, 56 (5), 1402-1407. doi: 10.1016/j.camwa.2008.03.003
  20. Tavakoli M., Rahbarnia F., Ashrafi A.R. Some new results on irregularity of graphs. J. Appl. Math. Inf. 2014, 32, 675-685. doi: 10.14317/jami.2014.675
  21. Veylaki M., Nikmehr M.J., Tavallaee H.A. The third and hyper-Zagreb coindices of some graph operations. J. Appl. Math. Comput. 2016, 50 (1), 315-325. doi: 10.1007/s12190-015-0872-z
  22. Eskender B., Vumar E. Eccentric connectivity index and eccentric distance sum of some graph operations. Trans. Comb. 2013, 2 (1), 103-111.
  23. De N., Nayeem S.M.A., Pal A. Total eccentricity index of the generalized hierarchical product of graphs. Int. J. Appl. Comput. Math. 2015, 1 (3), 503-511. doi: 10.1007/s40819-014-0016-4
  24. Pattabiraman K., Kandan P. Weighted PI index of corona product of graphs. Discrete Math. Algorithm. Appl. 2014, 6, article id 1450055. doi: 10.1142/S1793830914500554
  25. Alizadeh Y., Iranmanesh A., Doslić T., Azari M. The edge Wiener index of suspensions, bottlenecks, and thorny graphs. Glas. Mat. 2014, 49 (1), 1-12.
  26. Yarahmadi Z., Ashrafi A.R. The Szeged, Vertex PI, first and second Zagreb indices of corona product of graphs. Filomat 2012, 26 (3), 467-472.
  27. De N. On eccentric connectivity index and polynomial of thorn graph. Appl. Math. 2012, 3 (8), 931-934. doi: 10.4236/am.2012.38139
  28. De N. Augmented eccentric connectivity index of some thorn graphs. Intern. J. Appl. Math. Res. 2012, 1 (4), 671-680. doi: 10.14419/ijamr.v1i4.326