The first general Zagreb coindex of graph operations

[1]N. Trinajstic, (2018), Chemical graph theory, Routledge.TrinajsticN.2018Chemical graph theoryRoutledge10.1201/9781315139111Search in Google Scholar

[2]M.V. Diudea, I. Gutman, and L. Jantschi, (2001), Molecular topology, Huntington, NY: Nova Science Publishers.DiudeaM.V.GutmanI.JantschiL.2001Molecular topologyHuntington, NYNova Science PublishersSearch in Google Scholar

[3]H. Yousefi-Azari, B. Manoochehrian, A.R. Ashrafi, (2008), The PI index of product graphs, Appl. Math. Lett. 21(6), 624–627.Yousefi-AzariH.ManoochehrianB.AshrafiA.R.2008The PI index of product graphsAppl. Math. Lett.21662462710.1016/j.aml.2007.07.015Search in Google Scholar

[4]M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, (2008), The hyper-Wiener index of graph operations. Comput. Math. Appl. 56(5), 1402–1407.KhalifehM.H.Yousefi-AzariH.AshrafiA.R.2008The hyper-Wiener index of graph operationsComput. Math. Appl.5651402140710.1016/j.camwa.2008.03.003Search in Google Scholar

[5]W. Gao, M.K. Jamil, M.R. Farahani, (2017), The hyper-Zagreb index and some graph operations. Journal of Applied Mathematics and Computing. 54(1–2), 263–275.GaoW.JamilM.K.FarahaniM.R.2017The hyper-Zagreb index and some graph operationsJournal of Applied Mathematics and Computing541–226327510.1007/s12190-016-1008-9Search in Google Scholar

[6]B. Basavanagoud, and S. Patil, (2016), A note on hyper-Zagreb index of graph operations, Iranian Journal of mathematical chemistry. 7(1), 89–92.BasavanagoudB.PatilS.2016A note on hyper-Zagreb index of graph operationsIranian Journal of mathematical chemistry718992Search in Google Scholar

[7]N. De, S. Nayeem, and A. Pal, (2015), Reformulated first Zagreb index of some graph operations. Mathematics. 3(4), 945–960.DeN.NayeemS.PalA.2015Reformulated first Zagreb index of some graph operationsMathematics3494596010.3390/math3040945Search in Google Scholar

[8]I. Gutman, and N. Trinajstić, (1972), Graph theory and molecular orbitals total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett. (17) 535–538.GutmanI.TrinajstićN.1972Graph theory and molecular orbitals total π-electron energy of alternant hydrocarbonsChem. Phys. Lett.1753553810.1016/0009-2614(72)85099-1Search in Google Scholar

[9]B. Furtula, I. Gutman, (2015), A forgotten topological index, Journal of Mathematical Chemistry. 53(4), 1184–1190.FurtulaB.GutmanI.2015A forgotten topological indexJournal of Mathematical Chemistry5341184119010.1007/s10910-015-0480-zSearch in Google Scholar

[10]X. Li, and J. Zheng, (2005), A unified approach to the extremal trees for different indices. MATCH Commun. Math. Comput. Chem. 54(1), 195–208.LiX.ZhengJ.2005A unified approach to the extremal trees for different indicesMATCH Commun. Math. Comput. Chem.541195208Search in Google Scholar

[11]T. Došlić, (2008), Vertex-weighted Wiener polynomials for composite graphs. Ars Mathematica Contemporanea. 1(1), 66–80. https://doi.org/10.26493/1855-3974.15.895DošlićT.2008Vertex-weighted Wiener polynomials for composite graphsArs Mathematica Contemporanea116680https://doi.org/10.26493/1855-3974.15.89510.26493/1855-3974.15.895Search in Google Scholar

[12]N. De, S. M. A. Nayeem, A. Pal, (2016), F-index of some graph operations. Discrete Mathematics, Algorithms and Applications. 8(02), 1650025. https://doi.org/10.1142/S1793830916500257DeN.NayeemS. M. A.PalA.2016F-index of some graph operationsDiscrete Mathematics, Algorithms and Applications8021650025. https://doi.org/10.1142/S179383091650025710.1142/S1793830916500257Search in Google Scholar

[13]A. Graovac, and T. Pisanski, (1991), On the Wiener index of a graph. Journal of mathematical chemistry. 8(1), 53–62.GraovacA.PisanskiT.1991On the Wiener index of a graphJournal of mathematical chemistry81536210.1007/BF01166923Search in Google Scholar

[14]M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, (2009), The first and second Zagreb indices of some graph operations. Discrete Applied Mathematics. 157(4), 804–811.KhalifehM. H.Yousefi-AzariH.AshrafiA. R.2009The first and second Zagreb indices of some graph operationsDiscrete Applied Mathematics157480481110.1016/j.dam.2008.06.015Search in Google Scholar

[15]M. Azari, A. Iranmanesh, (2013), Computing the eccentric-distance sum for graph operations, Discrete Applied Mathematics. 161(18), 2827–2840.AzariM.IranmaneshA.2013Computing the eccentric-distance sum for graph operationsDiscrete Applied Mathematics161182827284010.1016/j.dam.2013.06.003Search in Google Scholar

[16]N. De, A. Pal, S. Nayeem, M. Abu, (2014), On some bounds and exact formulae for connective eccentric indices of graphs under some graph operations. International Journal of Combinatorics. 2014.DeN.PalA.NayeemS.AbuM.2014On some bounds and exact formulae for connective eccentric indices of graphs under some graph operationsInternational Journal of Combinatorics201410.1155/2014/579257Search in Google Scholar

[17]A.R. Ashrafi, T. Došliæ, and A. Hamzeh, (2010), The Zagreb coindices of graph operations. Discrete applied mathematics. 158(15), 1571–1578. https://doi.org/10.1016/j.dam.2010.05.017AshrafiA.R.DošliæT.HamzehA.2010The Zagreb coindices of graph operationsDiscrete applied mathematics1581515711578https://doi.org/10.1016/j.dam.2010.05.01710.1016/j.dam.2010.05.017Search in Google Scholar

[18]W. Imrich, and S. Klavzar, (2000), Product graphs: structure and recognition. John Wiley and Sons, New York.ImrichW.KlavzarS.2000Product graphs: structure and recognitionJohn Wiley and SonsNew YorkSearch in Google Scholar

[19]N. De, S. M. A. Nayeem, A. Pal, (2016), The F-coindex of some graph operations. SpringerPlus. 5(1), 221.DeN.NayeemS. M. A.PalA.2016The F-coindex of some graph operationsSpringerPlus5122110.1186/s40064-016-1864-7477167527026915Search in Google Scholar

[20]B. Basavanagoud, S. Patil, (2017), A note on hyper-Zagreb coindex of graph operations. J. Appl. Math. Comput. 53, 647–655.BasavanagoudB.PatilS.2017A note on hyper-Zagreb coindex of graph operationsJ. Appl. Math. Comput.5364765510.1007/s12190-016-0986-ySearch in Google Scholar

[21]N. De, A. Pal, SMA Nayeem, (2016), The irregularity of some composite graphs. Int. J. Appl. Comput. Math. 2(3), 411–420.DeN.PalA.NayeemSMA2016The irregularity of some composite graphsInt. J. Appl. Comput. Math.2341142010.1007/s40819-015-0069-zSearch in Google Scholar

[22]M. Veylaki, M. J. Nikmehr, A. Tavallaee, (2016), The third and hyper-Zagreb coindices of some graph operations. Journal of Applied Mathematics and Computing. 50(1–2), 315–325.VeylakiM.NikmehrM. J.TavallaeeA.2016The third and hyper-Zagreb coindices of some graph operationsJournal of Applied Mathematics and Computing501–231532510.1007/s12190-015-0872-zSearch in Google Scholar

[23]M. Azari, (2014), Sharp lower bounds on the Narumi-Katayama index of graph operations. Applied Mathematics and Computation. 239, 409–421.AzariM.2014Sharp lower bounds on the Narumi-Katayama index of graph operationsApplied Mathematics and Computation23940942110.1016/j.amc.2014.04.088Search in Google Scholar