Abstract
The second Zagreb index M 2(G) of a (molecule) graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we give sharp upper and lower bounds on the second Zagreb index of unicyclic graphs with n vertices and k pendant vertices. From which, \(U_{n-3}^n\) and C n have the maximum and minimum the second Zagreb index among all unicyclic graphs with n vertices, respectively.
Similar content being viewed by others
References
Gutman I., and Trinajstić N. (1972). Chem. Phys. Lett. 17:535
Balaban A.T., Motoc I., Bonchev D., and Mekenyan O. (1983). Topics Curr. Chem. 114:21
Gutman I., and Das K.C. (2004). MATCH Commun. Math Comput. Chem. 50:83
Gutman I., Ruščić B., Trinajstić N. and Wilcox C.F. (1975). J. Chem. Phys. 62:3399
Kier L.B., and Hall L.H. (1976). Molecular Connectivity in Chemistry and Drug Research. Academic Press, San Francisco
Kier L.B., and Hall L.H. (1986). Molecular Connectivity in Structure-Activity Analysis. Wiley, New York
Nikolić S., Kovačević G. and Trinajstić N. (2003). Croat. Chem. Acta 76:113
Todeschini R., and Consonni V. (2000). Handbook of Molecular Descriptors. Wiley-VCH, Weinheim
Das K.C., and Gutman I. (2005). MATCH Commun. Math Comput. Chem. 53:103
Liu B., and Guttman I. (2006). MATCH Commun. Math. Comput. Chem. 55:439
Zhang H., and Zhang S. (2006). MATCH Commun. Math Comput. Chem. 55:427
Zhou B. (2004). MATCH. Commun. Math. Comput. Chem. 52:113
Zhou B., and Guttman I. (2005). MATCH Commun. Math. Comput. Chem. 54:233
Bondy J.A., and Murty U.S. (1976). Graph Theory and its Applications. The Macmillan Press, London
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yan, Z., Liu, H. & Liu, H. Sharp Bounds for the Second Zagreb Index of Unicyclic Graphs. J Math Chem 42, 565–574 (2007). https://doi.org/10.1007/s10910-006-9132-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-006-9132-7