The “pentachains” studied in this paper are graphs formed of concatenated 5-cycles. Explicit formulas are obtained for the Schultz and modified Schultz indices of these graphs, as well as for generalizations of these indices. In the process we give a more refined version of the procedure that earlier was reported for the ordinary Wiener index.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Yang B.-Y., Yeh Y.-N. (1995). Adv. Appl. Math. 16, 72
Gutman I. (1994). J. Chem. Inf. Comput. Sci. 34, 1087
Schultz H.P. (1989). J. Chem. Inf. Comput. Sci. 29, 227
Eu S.-P., Yang B.-Y., Yeh Y.-N. (2006). Int. J. Quant. Chem. 106, 426
Huang W.-C., Yang B.-Y., Yeh Y.-N. (1997). Discrete Appl. Math. 73, 113
Wiener H., (1947). J. Am. Chem. Soc. 69, 17
Hosoya H. (1971). Bull. Chem. Soc. Jpn. 44, 2332
Gutman I., Körtvélyesi T. (1995). Z. Naturforsch. 50a, 669
Todeschini R., Consonni V. (2000). Handbook of Molecular Descriptors. Wiley–VCH, Weinheim
Gutman I., Yeh Y.-N., Lee S.-L., Luo Y.-L. (1993). Indian J. Chem. 32A, 651
Dobrynin A.A., Entringer R., Gutman I. (2001). Acta Appl. Math. 66, 211
Dobrynin A.A., Gutman I., Klavžar S., Žigert P. (2002). Acta Appl. Math. 72, 247
D.H. Rouvray, in: Topology in Chemistry – Discrete Mathematics of Molecules, D.H. Rouvray and R.B. King eds. (Horwood, Chichester, 2002), pp. 1–15.
Buckley F., Harary F. (1990). Distances in Graphs. Addison–Wesley, New York
Gutman I. (1987). Chem. Phys. Lett. 136, 134
Gutman I., Kennedy J.W., Quintas L.V. (1990). Chem. Phys. Lett. 173, 403
Polansky O.E., Randić M., Hosoya H. (1989). MATCH Commun. Math. Comput. Chem. 24, 3
Huang I.-W., Yang B.-Y., Yeh Y.-N. (1996). Southeast Asia Bull. Math. 20, 81
B.-Y. Yang and Y.-N. Yeh, in: Proceedings of the First International Tainan–Moscow Algebra Workshop, eds. Y. Fong et al. (de Gruyter, Berlin, 1996), pp. 329–349.
Yang B.-Y., Yeh Y.-N. (2004). Stud. Appl. Math. 112, 333
B.-Y. Yang and Y.-N. Yeh, in: Proceedings of the Second International Tainan–Moscow Algebra Workshop, Tainan, 1998, Y. Fong et al. eds. (Springer, Hong Kong, 2000), pp. 203–226.
Yang B.-Y., Yeh Y.-N. (2004). Int. J. Quantum. Chem. 99, 80
Tratch S.S., Stankevich M.I., Zefirov N.S. (1990). J. Comput. Chem. 11, 899
Mihalić Z., Nikolić S., Trinajstić N. (1992). J. Chem. Inf. Comput. Sci. 32, 28
Randić M. (1993). Chem. Phys. Lett. 211, 478
Randić M., Guo X., Oxley T., Krishnapriyan H., Naylor L. (1994). J. Chem. Inf. Comput. Sci. 34, 361
Khadikar P.V., Deshpande N.V., Kale P.P., Dobrynin A., Gutman I., Dömötör G. (1995). J. Chem. Inf. Comput. Sci. 35, 547
Zhu H.Y., Klein D.J., Lukovits I. (1996). J. Chem. Inf. Comput. Sci. 36, 420
Gutman I., Mohar B. (1996). J. Chem. Inf. Comput. Sci. 36, 982
Lukovits I. (1998). J. Chem. Inf. Comput. Sci. 38, 125
Klein D.J., Gutman I. (1999). J. Chem. Inf. Comput. Sci. 39, 534
Gutman I., Linert W., Lukovits I., Tomović Ž. (2000). J. Chem. Inf. Comput. Sci. 40, 113
Ivanciuc O., Ivanciuc T., Klein D.J., Seitz W.A., Balaban A.T. (2001). J. Chem. Inf. Comput. Sci. 41, 536
Bonchev D. (2001). J. Chem. Inf. Comput. Sci. 41, 582
Li X., Lin J. (2002). J. Chem. Inf. Comput. Sci. 42, 1358
Li X., Lin J. (2003). J. Math. Chem. 33, 81
Randić M. (2004). J. Chem. Inf. Comput. Sci. 44, 373
Li X., Hu M., Xiao H. (2004). J. Chem. Inf. Comput. Sci. 44, 508
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gutman, I., Yan, W., Yeh, YN. et al. Generalized Wiener indices of zigzagging pentachains. J Math Chem 42, 103–117 (2007). https://doi.org/10.1007/s10910-006-9078-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-006-9078-9