On the zagreb indices of the line graphs of polyphenylene dendrimers

References

• A. Iranmanesh, N.A. Gholami, Computing the Szeged index of styrylbenzene dendrimer and triarylamine dendrimer of generation 1-3, MATCH Commun. Math. Comput. Chem., 62 (2009), 371-379.
   Web of Science ®Google Scholar
• A.R. Ashrafi, M. Mirzargar, PI, Szeged, and edge Szeged indices of an infinite family of nanostars dendrimers, Indian J. Chem., 47A (2008), 538-541.
   Google Scholar
• A.R. Ashrafi, T. DoŠlić, A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010) 1571-1578. DOI:10.1016/j.dam.2010.05.017
   Web of Science ®Google Scholar
• A.R. Ashrafi, T. DoŠlić, A. Hamzeh, Extremal graphs with respect to the Zagreb coindices, MATCH Commun. Math. Comput.Chem. 65 (2011) 85-92.
   Web of Science ®Google Scholar
• B. Liu, I. Gutman, Upper bounds for Zagreb indices of connected graphs, MATCH Commun. Math. Comput. Chem. 55 (2006), 439-446.
   Web of Science ®Google Scholar
• F. Harary, Graph Theory, Addison-Wesely, Reading, 1969, DOI:10.1201/9780429493768.
   Google Scholar
• G. Caporossi, P. Hansen, D. Vukićević, Comparing Zagreb indices of cyclicgraphs, MATCH Commun. Math. Comput. Chem. 63 (2010), 441-451.
   Web of Science ®Google Scholar
• G. H. Fath-Tabar, Old and new Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 65 (2011) 79-84.
   Web of Science ®Google Scholar
• I. Gutmnan, B. Furtula, On Zagreb Indices and coindices, MATCH Commun. Math. Comput. Chem. 74 (2015), 5–16.
   Web of Science ®Google Scholar
• I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total p-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538, DOI: 10.1016/0009-2614(72)85099-1.
   Web of Science ®Google Scholar
• I. Gutman, Y. N. Lee, Y. N. Yeh, Y. L. Lau, Some recent results in the theory of Wiener number, Ind. J. Chem. 32 (1993) 551–661.
   Web of Science ®Google Scholar
• K.C. Das, I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem 52 (2004) 103-112.
   Google Scholar
• M.A. Rajan, V. Lokesha, P.S. Ranjini, A Study on Series Edge Graph Transformation, in: Proc. 23rd Joint Congress Iran-South Korea Jangjeon Math. Soc., Iran, 2010.
   Google Scholar
• M. Mirzagar, PI, Szeged and edge Szeged polynomials of a dendrimer nanostar, MATCH Commun. Math. Comput. Chem., 62 (2009), 363-370.
   Web of Science ®Google Scholar
• M. Randić, On characterization on molecular branching, J. Am. Chem. Soc. 97 (1975), 6609-6615. DOI:10.1021/ja00856a001
   Web of Science ®Google Scholar
• M. Velaki, M. V. Nikmehr, H.A. Tavallaee, The third and hyper-Zagreb coindices of some graph operations, J. Appl. Math. Comput. 50, (2016) 315-325. DOI:10.1007/s12190-015-0872-z
   Google Scholar
• N. Trinajstić, Chemical Graph Theory. Vol 1 and 2, CRC Press, Boca Raton, FL., USA.
   Google Scholar
• P.S. Ranjini, V. Lokesha, M.A. Rajan, On Zagreb indices of the subdivision graphs, Int. J. Math. Sci. Eng. Appl. vol. 4 (2010) 221–228.
   Google Scholar
• P.S. Ranjini, V. Lokesha, I. N. Cangul, On Zagreb indices of the line graphs of the subdivision, App. Math. Comput., Vol 218 (2011) 699-702. https://doi.org/10.1016/j.amc.2011.03.125
   Web of Science ®Google Scholar
• R. Todeschini, V. Consomi, Hnadbook of Molecular Descriptor, Wiley-VCH, Weinhein, 2000, DOI: 10.1002/9783527613106.
   Google Scholar
• S. Alikhani, M.A. Iranmanesh, Chromatic polynomials of some dendrimers, J. Comput. Theor. Nanosci, 7(11) (2010), 2314-2316. DOI:10.1166/jctn.2010.1613
   Google Scholar
• S. Alikhani, M.A. Iranmanesh, Chromatic polynomials of some nanostars, Iranian Journal of Math. Chemist. Vol. 3, No. 2 (2012), 127-135. DOI:10.22052/ijmc.2012.5232
   Google Scholar
• S. M. Hosamani, B. Basavanagoud, New upper bounds for the first Zagreb index, MATCH Commun. Math. Comput. Chem. 74(1) (2015) 97–101.
   Web of Science ®Google Scholar
• S. M. Hosamani and I. Gutman, Zagreb indices of transformation graphs and total transformation graphs, Appl. Math. Comput. 247 (2014) 1156-1160. DOI: /10.1016/j.amc.2014.09.080
   Web of Science ®Google Scholar
• T. Došlić, Vertex weighted Wiener polynomials for composite graphs, Ars Mathematics Contemporaneity 1(2008) 66-80, DOI: 10.26493/1855-3974.15.895.
   Web of Science ®Google Scholar
• Z. Yan, H. Liu, H. Liu, Sharp bounds for the second Zagreb index of unicyclic graphs, J. Math. Chem. 42 (2007), 565-574, DOI: 10.1007/s10910-006-9132-7.
   Web of Science ®Google Scholar
• X. Zhang, A. Razzaq, K. Ali, S.T.R. Rizvi, M.R. Farahani. A new approach to find eccentric indices of some graphs. Journal of Information & Optimization Sciences. 41(4), 2020, 865–877. DOI:10.1080/02522667.2020.1744304
   Web of Science ®Google Scholar
• M.S. Sardar, S-A. Xu, W. Sajjad, S. Zafar, I.N. Cangul, M.R. Farahani. An explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNCk[n], Journal of Information and Optimization Sciences, 41(4), 2020, 879–890 DOI:10.1080/02522667.2020.1753304
   Web of Science ®Google Scholar
• M.N. Husin, F. Asif, Z. Zahid, S. Zafar. On topological properties of some convex polytopes by using line operator on their subdivisions, Journal of Information and Optimization Sciences, 41(4), 2020, 891–903 DOI:10.1080/02522667.2020.1744305
   Web of Science ®Google Scholar
• Z. Ahmad, A.Q. Baig, M.R. Azhar, M. Imran. Total eccentricity and average eccentricity indices of some chemical graphs: Carbon graphite and copper oxide. Journal of Information and Optimization Sciences, 41(4), 2020, 905–924. DOI:10.1080/02522667.2020.1745379
   Web of Science ®Google Scholar
• M. Cancan, S. Ediz, S. Fareed, M.R. Farahani. More topological indices of generalized prism network, Journal of Information and Optimization Sciences, 41(4), 2020, 925–932 DOI:10.1080/02522667.2020.1748273
   Web of Science ®Google Scholar
• M. Alaeiyan, F. Afzal, M.R. Farahani, M.A. Rostami. An exact formulas for the Wiener polarity index of nanostar dendrimers, Jour- nal of Information and Optimization Sciences, 41(4), 2020, 933–939. DOI:10.1080/02522667.2020.1748274
   Web of Science ®Google Scholar
• M.N. Husin, A. Ariffin, M. Alaeiyan. The neighbourhood polynomial of certain networks, Journal of Information and Optimization Sciences, 41(4), 2020, 941–948. DOI:10.1080/02522667.2020.1748275
   Web of Science ®Google Scholar
• M. Cancan, S. Ediz, M. Alaeiyan, M.R. Farahani. On Ve-degree molecular properties of copper oxide. Journal of Information and Optimization Sciences, 41(4), 2020, 949–957. DOI:10.1080/02522667.2020.1747191
   Web of Science ®Google Scholar
• W. Sajjad, M.S. Sardar, M. Cancan, S. Ediz, A.Q. Baig. On modified eccentric connectivity index of nanotube, Journal of Information and Optimization Sciences, 41(4), 2020, 959–972. DOI:10.1080/02522667.2020.174538.
   Web of Science ®Google Scholar