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Abstract
In this paper we computed explicit formulas for the edge version of harmonic index and harmonic polynomial of some classes of rooted product of graphs and i-th vertex rooted product of graphs.
References
Harris I, John M. Combinatorics and Graph Theory. New York: Springer-Verlag 2000.
Gross J, Yellen T. Graph Theory and Its Applications, 2nd ed. Boca Raton, FL: CRC Press 2006.
Bertz SH. The bond graph. J.C.S. Chem Commun 1981; 818-820. https://doi.org/10.1039/c39810000818
Gutman I, Popovic L, Mishra BK, Kaunar M, Estrada E, Guevara N. Application of line graphs in physical chemistry. Predicting surface tension of alkanes. J Serb Chem Soc 1997; 62: 1025-1029.
Gutman I, Tomovic Z. On the application of line graphs in quantitative structure-property studies. J Serb Chem Soc 2000; 65(8): 577-580.
Gutman I, Tomovic Z. Modeling boiling points of cycloalkanes by means of iterated line graph sequences. J Chem Inf Comput Sci 2001; 41: 1041-1045. https://doi.org/10.1021/ci010006n
Li X, Gutman I. Mathematical Aspects of Randic-Type Molecular Structure Descriptors, University of Kragujevac, Kragujevac 2006.
Godsil CD, McKay BD. A new graph product and its spectrum 1978.
Gutman I, Furtula B. Recent Results in the Theory of Randic Index, University of Kraguje-vac, Kragujevac 2008.
Li X, Shi Y. A survey on the Randic index, MATCH Commun. Math Comput Chem 2008; 59: 127-156.
Tomescu I, Marinescu-Ghemeci R, Mihai G. On dense graphs having minimum Randic index. Romanian J Inf Sci Tech 2009; 12: 455-465.
Das KC, Sorgun S. On Randic energy of graphs. MATCH Commun Math Comput Chem 2014; 72: 227-238.
Zhou B, Trinajsti N. On a novel connectivity index. J Math Chem 2009; 46: 12521270. https://doi.org/10.1007/s10910-008-9515-z
Baca M, Horvthov J, Mokriov M, Suhnyiov A. On topological indices of fullerenes. Appl Math Comput 2015; 251: 154-161. https://doi.org/10.1016/j.amc.2014.11.069
Chen J, Liu J, Guo X. Some upper bounds for the atom-bond connectivity index of graphs. Appl Math Lett 2012; 25: 1077-1081. https://doi.org/10.1016/j.aml.2012.03.021
Das KC, Gutman I, Furtula B. On atom-bond connectivity index. Chem Phys Lett 2011; 511: 452-454. https://doi.org/10.1016/j.cplett.2011.06.049
Du Z, Zhou B, Trinajsti N. Minimum general sum-connectivity index of unicyclic graphs. J Math Chem 2010; 48: 697-703. https://doi.org/10.1007/s10910-010-9702-6
Hayat S, Imran M. Computation of topological indices of certain networks. Appl Math Com-put 2014; 240: 213-228. https://doi.org/10.1016/j.amc.2014.04.091
Hayat S, Imran M, Mailk MYH. On topological indices of certain interconnection net-works. Appl Math Comput 2014; 244: 936-951. https://doi.org/10.1016/j.amc.2014.07.064
Li X, Shi Y, Wang L. An updated survey on the Randic index, in: B.F. I. Gutman (Ed.), Recent Results in the Theory of Randic Index, University of Kragujevac and Faculty of Science Kragujevac 2008; 9-47.
Nadeem MF, Zafar S, Zahid Z. Certain topological indicies of the line graph of subdivsion graphs. Appl Math Comput 2015; 271: 790-794. https://doi.org/10.1016/j.amc.2015.09.061
Nadeem MF, Zafar S, Zahid Z. On Topological properties of the line graph of subdivision graphs of certain nanostructures. Appl Math Comput 2016; 273: 125-130. https://doi.org/10.1016/j.amc.2015.10.010
Iranmanesh MA, Saheli M. On the harmonic index and harmonic polynomial of Caterpillars with diameter four. Iranian J of Math Chem 2015; 6(1): 41-49.
Nazir R, Sardar S, Zafar S, Zahid Z. Edge version of harmonic polynomial and harmonic index. Journal of Applied Mathematics and Informatics 2016; 34: 479-486. https://doi.org/10.14317/jami.2016.479
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