Certain topological indices and polynomials for the Isaac graphs

References

• K. Chuda. S(2,1)-labeling of graphs with cyclic structure, Acta U. Matthiae Belli, Series Mathematics, 18(2011), 29-33.
   Google Scholar
• R. Isaacs. Infinite families of nontrivial trivalent graphs which are not Tait colorable, The American Mathematical Monthly, 82(3)(1975), 221-239. DOI:10.1080/00029890.1975.11993805
   Web of Science ®Google Scholar
• I. Gutman and N. Trinajstić. Graph theory and molecular orbitals, Total f -electron energy of alternant hydrocarbons. Chemical Physics Letters, 17(4)(1972), 535-538. DOI:10.1016/0009-2614(72)85099-1.
   Web of Science ®Google Scholar
• G. H. Fath-Tabar, Old and new Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem, 65(1)(2011), 79-84.
   Web of Science ®Google Scholar
• G. H. Fath-Tabar, Zagreb polynomial and PI indices of some nanostructures, Digest Journal of Nanomaterials & Biostructures (DJNB), 4(1)(2009), 181-191.
   Web of Science ®Google Scholar
• J. Hao, Propositions about Zagreb indices and modified Zagreb indices, MATCH Commun. Math. Comput. Chem, 65(2011), 659-670.
   Web of Science ®Google Scholar
• G. H. Shirdel, H. Rezapour, and A.M. Syadi. The hyper-Zagreb index of graph operations, Iranian J. Math. Chem, 4(2)(2013), 213-220. DOI:10.22052/IJMC.2013.5294
   Google Scholar
• B. Furtula, and I. Gutman, A forgotten topological index. Journal of Mathematical Chemistry, 53(4)(2015), 1184-1190. DOI:10.1007/s10910-015-0480-z
   Google Scholar
• M. Randic, On characterization of molecular branching, J. Amer. chem. Soc, 97(1975), 6609-6615. DOI:10.1021/ja00856a001
   Web of Science ®Google Scholar
• B. Bollobas, and P. Erdos. Graphs of extremal weights, Ars Combin, 50(1998), 225-233.
   Web of Science ®Google Scholar
• I. Gutman, B. Furtula, and C. Elphick. Three new/old vertex-degree based topological indices, MATCH Commun. Math. Comput. Chem, 72(24)(2014), 617-632.
   Google Scholar
• E. Estrada, L. Torres, L. Rodriguez, and I. Gutman, An atom-bond connectivity index:modelling the enthalpy of formation of alkanes, Indian journal of chemistry. Sect. A: Inorganic, physical, theoretical and analytical, 37(10)(1998), 849-855.
   Google Scholar
• D. Vukičević, and B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem, 46(2009), 1369-1376. DOI:10.1007/s10910-009-9520-x
   Web of Science ®Google Scholar
• S. Fajtlowicz, On conjectures of Graffiti-II. Congr. Numer, 60(1987), 187-197.
   Google Scholar
• D. Vukičević, and M. Gašperov, Bond additive modeling 1. Adriatic indices. Croatica chemica acta, 83(3)(2010), 243-260.
   Web of Science ®Google Scholar
• V. R. Kulli, The Guava indices and indices of graphs, Annals of Pure and Applied Mathematics, 14(1)(2017), 33-38. doi: 10.22457/apam.v14n1a4
   Google Scholar
• V. R. Kulli, The product connectivity Gourava index, Journal of Computer and Mathematical Sciences, 8(6)(2017), 235-242.
   Google Scholar
• V. R. Kulli, On the sum connectivity Gourava index, International Journal of Mathematical Archive, 8(6)(2017), 211-217.
   Google Scholar
• V. R. Kulli, On Hyper Gourava indices and coindices, International Journal of Mathematical Archive, 8(12)(2017), 116-120.
   Google Scholar
• P. S. Ranjini, V. Lokesha, and A. Usha, Relation between phenylene and hexagonal squeeze using harmonic index, Int. J. Graph Theory, 1 (4)(2013), 116-121.
   Google Scholar
• C.T. Martínez-Martínez, J.A. Méndez-Bermúdez, J.M. Rodríguez, and J.M. Sigarreta, Computational and analytical studies of the Randić index in Erdös-Rényi models, Applied Mathematics and Computation, 377(2020), 125137. DOI:10.1016/j.amc.2020.125137
   Web of Science ®Google Scholar
• A. J. M. Khalaf, A. Javed, M. K. Jamil, M. Alaeiyan, and M. R. Farahani, Topological properties of four types of porphyrin dendrimers. Proyecciones (Antofagasta), 39(4)(2020), 979-993. doi: 10.22199/issn.0717-6279-2020-04-0061
   Google Scholar
• W. Gao, and M. R. Farahani. The hyper-Zagreb index for an infinite family of nanostar dendrimer. Journal of Discrete Mathematical Sciences and Cryptography, 20(2)(2017), 515-523. DOI:10.1080/09720529.2016.1220088
   Web of Science ®Google Scholar
• A. J. M. Khalaf, M. F. Hanif, M. K. Siddiqui, and M.R. Farahani, On degree based topological indices of bridge graphs. Journal of Discrete Mathematical Sciences, Cryptography, 23(6)(2020), 1139-1156. DOI:10.1080/09720529.2020.1822040
   Google Scholar
• X. Zhang, X. Wu, S. Akhter, M. K. Jamil, J.B. Liu, and M.R. Farahani. Edge-version atom-bond connectivity and geometric arithmetic indices of generalized bridge molecular graphs. Symmetry, 10(12) (2018), 751. DOI:10.3390/sym10120751
   Google Scholar
• D. X. Li,, J. B. Liu, and S. M. Hosamani, B. Basavanagoud, and M.R. Farahani, Zagreb Indices of Semi-Total (Total) Block Graphs of Bridge and Chain Graphs, Journal of Computational and Theoretical Nanoscience, 14(6) (2017), 2777-2780. DOI:10.1166/jctn.2017.6574
   Google Scholar
• A. Asok, and J.V. Kureethara, The QSPR Study of Butane Derivatives: A Mathematical Approach, Oriental Journal of Chemistry, 34(4)(2018), 1842-1846. DOI:10.13005/ojc/3404018
   Web of Science ®Google Scholar
• N. De, M. Cancan, and M. Alaeiyan, On some degree based topological indices of mk-graph, Journal of Discrete Mathematical Sciences, Cryptography. 23(6)(2020), 1183-1194. DOI:10.1080/09720529.2020.1809112
   Google Scholar
• U. K. Faraji, M. Alaeiyan, M. Golriz, and A.R. Gilani, Harmonic indices of polyhex zigzag TUZC6[m; n] nanotube and nanotori, Journal of Information and Optimization Sciences, 41(4)(2020), 1093-1100. DOI:10.1080/02522667.2020.1744309
   Web of Science ®Google Scholar
• H. S. Ramane, S.Y. Talwar, and I.N. Cangul, Transmission and Reciprocal Transmission Based Topological Co-Indices of Graphs, European Journal of Pure and Applied Mathematics, 13(5)(2020), 1057-1071. DOI:10.29020/nybg.ejpam.v13i5.3724
   Web of Science ®Google Scholar
• A.W.R. Bharati, C. Grigorious, and S. Stephen, On certain topological indices of silicate, honeycomb and hexagonal networks, Journal of Computer and Mathematical Sciences, 3(5)(2012), 498-556.
   Google Scholar
• N. H. A. M. Saidi, M. Nazri Husin, and N. B. Ismail, On the Zagreb indices of the line graphs of Polyphenylene Dendrimers, Journal of Discrete Mathematical Sciences and Cryptography, 23(6)(2020), 1239-1252. DOI:10.1080/09720529.2020.1822041
   Web of Science ®Google Scholar
• I. Gutman, B. Furtula, and V. Katanić, Randić index and information, AKCE International Journal of Graphs and Combinatorics, 15(3)(2018), 307-312. DOI:10.1016/j.akcej.2017.09.006
   Web of Science ®Google Scholar
• Ö. Ç. Havare. On the inverse sum indeg index of some graph operations, Journal of the Egyptian Mathematical Society, 28(1)(2020), 1-11. DOI:10.1186/s42787-020-00089-1
   Google Scholar
• K. C. Das, J. M. Rodríguez, and J. M. Sigarreta, On the maximal general ABC index of graphs with given maximum degree, Applied Mathematics and Computation, 386(2020), 125531. DOI:10.1016/j.amc.2020.125531
   Web of Science ®Google Scholar
• U. K. Faraji, M. Alaeiyan, M. Golriz, and A.R. Gilani, Harmonic indices of polyhex zigzag TUZC6[m; n] nanotube and nanotori, Journal of Information and Optimization Sciences, 41(4)(2020), 1093-1100. doi: 10.1080/02522667.2020.1744309
   Web of Science ®Google Scholar
• S. Kanwal, M. Imtiaz, A. Manzoor, N. Idrees, A. Afzal. Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph, Indonesian Journal of Combinatronics, 3(2) (2020), 63-78. DOI:10.19184/ijc.2019.3.2.1
   Google Scholar