×

Estimating the Szeged index. (English) Zbl 1177.05030

Summary: Lower and upper bounds on Szeged index of connected (molecular) graphs are established as well as Nordhaus-Gaddum-type results, relating the Szeged index of a graph and of its complement.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C12 Distance in graphs
05C90 Applications of graph theory
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gutman, I.; Polansky, O. E., Mathematical Concepts in Organic Chemistry (1986), Springer: Springer Berlin · Zbl 0657.92024
[2] Todeschini, R.; Consonni, V., Handbook of Molecular Descriptors (2000), Wiley-VCH: Wiley-VCH Weinheim
[3] Wiener, H., Structural determination of paraffin boiling points, J. Am. Chem. Soc., 69, 17-20 (1947)
[4] Gutman, I., A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N. Y., 27, 9-15 (1994)
[5] Gutman, I.; Dobrynin, A. A., The Szeged index — A success story, Graph Theory Notes N. Y., 34, 37-44 (1998)
[6] Khadikar, P. V.; Deshpande, N. V.; Kale, P. P.; Dobrynin, A.; Gutman, I., The Szeged index and an analogy with the Wiener index, J. Chem. Inf. Comput. Sci., 35, 547-550 (1995)
[7] Klavžar, S.; Rajapakse, A.; Gutman, I., The Szeged and the Wiener index of graphs, Appl. Math. Lett., 9, 45-49 (1996) · Zbl 0903.05020
[8] Khalifeh, M. H.; Yousefi-Azari, H.; Ashrafi, A. R., A matrix method for computing Szeged and vertex PI indices of join and composition of graphs, Linear Algebra Appl., 429, 2702-2709 (2008) · Zbl 1156.05034
[9] Yousefi-Azari, H.; Manoochehrian, B.; Ashrafi, A. R., Szeged index of some nanotubes, Curr. Appl. Phys., 8, 713-715 (2008) · Zbl 1224.05150
[10] Diudea, M. V.; Florescu, M. S.; Khadikar, P. V., Molecular Topology and its Applications (2006), EfiCon Press: EfiCon Press Bucharest
[11] Khadikar, P. V.; Karmarkar, S.; Agrawal, V. K.; Singh, J.; Shrivastava, A.; Lukovits, I.; Diudea, M. V., Szeged index — Applications for drug modelling, Lett. Drug. Des. Discov., 2, 606-624 (2005)
[12] Dobrynin, A. A.; Entringer, R.; Gutman, I., Wiener index of trees: Theory and applications, Acta Appl. Math., 66, 211-249 (2001) · Zbl 0982.05044
[13] Nordhaus, E. A.; Gaddum, J. W., On complementary graphs, Amer. Math. Monthly, 63, 175-177 (1956) · Zbl 0070.18503
[14] Zhang, L.; Wu, B., The Nordhaus-Gaddum-type inequalities for some chemical indices, MATCH Commun. Math. Comput. Chem., 54, 183-194 (2005) · Zbl 1084.05072
[15] Goodman, A. W., On sets of acquaintances and strangers at any party, Amer. Math. Monthly, 66, 778-783 (1959) · Zbl 0092.01305
[16] Gutman, I.; Trinajstić, N., Graph theory and molecular orbitals. Total \(\pi \)-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, 535-538 (1972)
[17] Das, K. C., Maximizing the sum of the squares of the degrees of a graph, Discrete Math., 285, 57-66 (2004) · Zbl 1051.05033
[18] Gutman, I.; Das, K. C., The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50, 83-92 (2004) · Zbl 1053.05115
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.