Browse > Article
http://dx.doi.org/10.14317/jami.2016.479

EDGE VERSION OF HARMONIC INDEX AND HARMONIC POLYNOMIAL OF SOME CLASSES OF GRAPHS  

NAZIR, RABIA (Department of Mathematics, University of Management and Technology (UMT))
SARDAR, SHOAIB (Department of Mathematics, University of Management and Technology (UMT))
ZAFAR, SOHAIL (Department of Mathematics, University of Management and Technology (UMT))
ZAHID, ZOHAIB (Department of Mathematics, University of Management and Technology (UMT))
Publication Information
Journal of applied mathematics & informatics / v.34, no.5_6, 2016 , pp. 479-486 More about this Journal
Abstract
In this paper we define the edge version of harmonic index and harmonic polynomial of a graph G. We computed explicit formulas for the edge version of harmonic index and harmonic polynomial of many well known classes of graphs.
Keywords
Topological indices; line graph;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S.H. Bertz, The bond graph, J.C.S. Chem. Commun. 1981, 818-820.   DOI
2 S. Fajtlowicz, On conjectures of Grafiti II, Congr. Numer. 60 (1987), 187-197.
3 O. Favaron, M. Maheo and J.F. Sacle, Some eigenvalue properties in graphs (conjectures of Grafiti II), Discrete Math. 111 (1993), 197-220.   DOI
4 I. Gutman, Edge versions of topological indices, in: I. Gutman and B. Furtula (Eds.), Novel Molecular Structure Descriptors - Theory and Applications II , Univ. Kragujevac 3 (2010).
5 I. Gutman and E. Estrada, Topological indices based on the line graph of the molecular graph, J. Chem. Inf. Comput. Sci. 36 (1996), 541-543.   DOI
6 I. Gutman, L. Popovic, B. K. Mishra, M. Kaunar, E. Estrada and N. Guevara, Application of line graphs in physical chemistry. Predicting surface tension of alkanes, J. Serb. Chem. Soc. 62 (1997), 1025-1029.
7 I. Gutman and Z. Tomovic, On the application of line graphs in quantitative structure-property studies, J. Serb. Chem. Soc. 65 (2000), 577-580.
8 I. Gutman and Z. Tomovic, Modeling boiling points of cycloalkanes by means of iterated line graph sequences, J. Chem. Inf. Comput. Sci. 41 (2001), 1041-1045.   DOI
9 A. Iranmanesh, I. Gutman, O. Khormali and A. Mahmiani, The edge versions of the Wiener index, MATCH Comm. Math. Comput. Chem. 61 (2009), 663-672.
10 M.A. Iranmanesh and M. Saheli, On the harmonic index and harmonic polynomial of Caterpillars with diameter four, Iranian J. of Math. Chem. 6 (2015), 41-49.
11 X. Li and Y. Shi, A survey on the Randic?index, MATCH Commun. Math. Comput. Chem. 59 (2008), 127-156.
12 X. Li, Y. Shi and L. Wang, 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.
13 V. Lokesha, A. Usha, P.S. Ranjini and T. Deepika, Harmonic Index of Cubic Polyhedral Graphs Using Bridge Graphs, Applied Mathematical Sciences 85 (2015), 4245-4253.   DOI
14 M.F. Nadeem, S. Zafar and Z. Zahid, Certain topological indicies of the line graph of subdivsion graphs, Appl. Math. Comput. 271 (2015), 790-794.   DOI
15 M.F. Nadeem, S. Zafar and Z. Zahid, On Topological properties of the line graph of subdivision graphs of certain nanostructures, Appl. Math. Comput. 273 (2016), 125-130.   DOI
16 J. Rada and R. Cruz, Vertex-degree-based topological indices over graphs, MATCH Commun. Math. Comput. Chem. 72 (2014), 603-616.
17 X. Xu, Relationships between harmonic index and other topological indices, Appl. Math. Sci. 6 (2012), 2013-2018.
18 P.S. Ranjini, V. Lokesha and A. Usha, Relation between Phenylene and Hexagonal Squeeze using Harmonic Index, International Journal of Graph Theory 1 (2013), 116-121.
19 B. Shwetha Shetty, V. Lokesha and P.S. Ranjini, On the Harmonic Index of Graph Operations, Transactions on Combinatorics 4 (2015), 5-14.
20 G. Yu and L. Feng, On connective eccentricity index of graphs, MATCH Commun. Math. Comput. Chem. 69 (2013), 611-628.
21 L. Zhong, The harmonic index for graphs, Appl. Math. Lett. 25 (2012), 561-566.   DOI
22 L. Zhong, The harmonic index on unicyclic graphs, Ars Combin. 104 (2012), 261-269.
23 L. Zhong and K. Xu, The harmonic index for bicyclic graphs, Utilitas Math. 90 (2013), 23-32.