Wiener, hyper-Wiener, detour and hyper-detour indices of bridge and chain graphs. (English) Zbl 1379.92077
Summary: Given a collection of connected graphs one may build bridge and chain graphs out of them. In this paper it is shown how the Wiener, hyper-Wiener, detour and hyper-detour indices for bridge and chain graphs are determined from the respective indices of the individual graphs. The results obtained are illustrated by some examples.
MSC:
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
| 05C90 | Applications of graph theory |
Keywords:
Wiener index; Hyper-Wiener index; detour index; Hyper-detour index; bridge graph; chain graphReferences:
| [1] | Amić D., Trinajstić N.: Croat. Chem. Acta 68, 53–62 (1995) |
| [2] | Balakrishnan R., Sridharan N., Viswanathan Iyer K.: Appl. Math. Lett. 21, 922–927 (2008) · Zbl 1152.05322 · doi:10.1016/j.aml.2007.10.003 |
| [3] | F. Buckley, F. Harary, Distance in Graphs. (Addison-Wesley, Reading, 1990) · Zbl 0688.05017 |
| [4] | D.M. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs, (Academic Press, 1980) · Zbl 0458.05042 |
| [5] | M.V. Diudea, I. Gutman, J. Lorentz, Molecular Topology. (Nova Science Publishers, 2001) |
| [6] | C. Godsil, G. Royle, Algebraic Graph Theory. (Springer, 2004) · Zbl 0968.05002 |
| [7] | Gutman I., Dobrynin A.A.: The Szeged index–a success story. Graph Theor. Notes N. Y. 34, 37–44 (1998) |
| [8] | I. Gutman, S. Klavzar, B. Mohar (eds.), Fifty years of the Wiener index. MATCH Commun. Math. Chem. 35, 1–259 (1997) |
| [9] | Gutman I., Linert W., Lukovits I., Dobrynin A.A.: J. Chem. Inf. Comput. Sci. 37, 349–354 (1997) |
| [10] | F. Harary, Graph Theory, (Addison-Wesley, Reading, 1969) |
| [11] | Ivanciue O., Trinajstić N.: Commun. Math. Comput. Chem. 30, 141–1522 (1994) |
| [12] | Khadikar P.V.: Natl. Acad. Sci. Lett. 23, 113–118 (2000) |
| [13] | Khadikar P.V., Deshpande N.V., Kale P.P., Dobrynin A., Gutman I.: J. Chem. Inf. Comput. Sci. 35, 547–550 (1995) |
| [14] | Khadikar P.V., Karmarkar S., Agrawal V.K.: Natl. Acad. Sci. Lett. 23, 165–170 (2000) |
| [15] | Klein D.J., Lukovits I., Gutman I.: J. Chem. Inf. Comput. Sci. 35, 50–52 (1995) |
| [16] | Lukovits I.: Comput. Chem. 19, 27–31 (1995) · Zbl 0820.92029 · doi:10.1016/0097-8485(94)00045-G |
| [17] | Lukovits I.: Croat. Chem. Acta 69, 873–882 (1996) |
| [18] | Lukovits I., Razinger M.: J. Chem. Inf. Comput. Sci. 37, 283–286 (1997) |
| [19] | Mansour T., Schork M.: MATCH Commun. Math. Chem. 61, 723–734 (2009) |
| [20] | T. Mansour, M. Schork, Discret. Appl. Math. (to appear) |
| [21] | Randić M.: Chem. Phys. Lett. 211, 478–483 (1993) · doi:10.1016/0009-2614(93)87094-J |
| [22] | Randić M., DeAlba L.M., Harris F.E.: Crat. Chem. Acta 71, 53–68 (1998) |
| [23] | Trinajstić N.: Chemical Graph Theory. CRC Press, Boca Raton (1983) |
| [24] | Trinajstić N., Nikolić S., Lucić B., Amić D., Mihalić Z.: J. Chem. Inf. Comput. Sci. 37, 631–638 (1997) |
| [25] | Trinajstić N., Nikolić S., Mihalić Z.: Int. J. Quantum Chem.: Quantum Chem. Symp. 65, 415–419 (1997) · doi:10.1002/(SICI)1097-461X(1997)65:5<415::AID-QUA6>3.0.CO;2-Z |
| [26] | Wiener H.: J. Am. Chem. Soc. 69, 17–20 (1947) · doi:10.1021/ja01193a005 |
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.
