[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2011.29.1_2.327

CALCULATION OF SOME TOPOLOGICAL INDICES OF SPLICES AND LINKS OF GRAPHS

Ashra, Ali Reza (Department of Mathematics, Statistics and Computer Science, University of Kashan)
Hamzeh, Asma (University of Kashan)
Hossein-Zadeh, Samaneh (School of Mathematics, Institute for Research in Fundamental Sciences (IPM))

Publication Information

Journal of applied mathematics & informatics / v.29, no.1_2, 2011 , pp. 327-335 More about this Journal

Abstract

Explicit formulas are given for the first and second Zagreb index, degree-distance and Wiener-type invariants of splice and link of graphs. As a consequence, the first and second Zagreb coindex of these classes of composite graphs are also computed.

Keywords

Wiener-type invariant; degree-distance; Zagreb index; Zagreb coindex; splice; link;

Citations & Related Records

Reference

1	S. Nikolic, G. Kovacevic, A. Milicevic, and N. Trinajstic, The Zagreb indices 30 years after, Croat. Chem. Acta, 76(2003), 113-124.
2	Sagan, B. E., Yeh, Y.-N. and Zhang, P. The Wiener polynomial of a graph, Int. J. Quant. Chem. 60 (5), 959-969, 1996. DOI ScienceOn
3	N. Trinajstic, Chemical Graph Theory, CRC Press, Boca Raton, FL. 1992.
4	H. Wiener, Structural determination of the paraffin boiling points, J. Am. Chem. Soc. 69 (1947), 17-20. DOI
5	H. Yousefi-Azari, M. Manoochehrian and A. R. Ashrafi, The PI index of product graphs, Appl. Math. Lett. 21(2008), 624-627. DOI ScienceOn
6	B. Zhou and I. Gutman, Relations between Wiener, hyper-Wiener and Zagreb indices, Chem. Phys. Lett. 394 (2004), 93-95. DOI
7	M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi and and S. G. Wagner, Some new results on distance-based graph invariants, European J. Combin. 30(2009), 1149-1163. DOI ScienceOn
8	M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi, A matrix method for computing Szeged and vertex PI indices of join and composition of graphs, Linear Algebra Appl. 429(2008), 2702-2709. DOI ScienceOn
9	M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi, The hyper-Wiener index of graph operations, Comput. Math. Appl. 56(2008), 1402-1407. DOI ScienceOn
10	M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi, Vertex and edge PI indices of Cartesian product graphs, Discrete Appl. Math. 156(2008), 1780-1789. DOI ScienceOn
11	I. Gutman K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92.
12	M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi and I. Gutman, The edge szeged index of product graphs, Croat. Chem. Acta, 81(2008), 277-281.
13	S. Klavzar, A. Rajapakse and I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett. 9 (1996), 45-49. DOI ScienceOn
14	S. Klavzar, On the PI index: PI-partitions and Cartesian product graphs, MATCH Commun. Math. Comput. Chem. 57(2007), 573-586.
15	I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34 (1994), 1087-1089. DOI
16	I. Gutman, A. A. Dobrynin, S. Klavzar and L. Pavlovic, Wiener-type invariants of trees and their relation, Bull. Inst. Combin. Appl. 40 (2004), 23-30.
17	A. Graovac and T. Pisanski, On the Wiener index of a graph, J. Math. Chem. 8 (1991), 53-62. DOI ScienceOn
18	A. A. Dobrynin and A. A. Kochetova, Degree distance of a graph: A degree analogue of the Wiener index, J. Chem. Inf. Comput. Sci. 34 (1994), 1082-1086. DOI
19	S. Hossein-Zadeh, A. Hamzeh and A. R. Ashrafi, Wiener-type invariants of some graph operations, FILOMAT 29(2009), 103-113.
20	M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157(2009), 804-811. DOI ScienceOn
21	T. Doslic, Splices, links, and their degree-weighted Wiener polynomials, Graph Theory Notes New York 48 (2005), 47-55.
22	T. Doslic, Vertex-Weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008), 66-80.
23	I. Gutman, A property of the Wiener number and its modifications, Indian J. Chem. 36A (1997), 128-132.
24	M. V. Diudea, I. Gutman and L. Jantschi, Molecular Topology, Huntington, New York, 2001.
25	I. Gutman and N. Trinajstic, Graph theory and molecular orbitals, Total $\pi$ electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538. DOI ScienceOn
26	A. R. Ashrafi, A. Hamzeh and S. Hossein-Zadeh, Computing Zagreb, Hyper-Wiener and Degree-Distance indices of four new sums of graphs, submitted.
27	A. R. Ashrafi, T. Doslic and A. Hamzeh, The Zagreb coindices of graph operation, Discrete Applied Mathematics (2010), doi:10.1016/j.dam.2010.05.017.