The Wiener number of a graph G is defined as 1/2∑d(u,v), where u,v ∈ V(G), and d is the distance function on G. The Wiener number has important applications in chemistry. We determine the Wiener number of an important family of graphs, namely, the Kneser graphs.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1402,
author = {Rangaswami Balakrishnan and S. Francis Raj},
title = {The Wiener number of Kneser graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {28},
year = {2008},
pages = {219-228},
zbl = {1156.05016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1402}
}
Rangaswami Balakrishnan; S. Francis Raj. The Wiener number of Kneser graphs. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 219-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1402/
[000] [1] R. Balakrishanan, N. Sridharan and K. Viswanathan, The Wiener index of odd graphs, Indian Inst. Sci. 86 (2006) 527-531. | Zbl 1226.05105
[001] [2] R. Balakrishanan, K. Viswanathan and K.T. Raghavendra, Wiener index of two special trees, MATCH Commun. Math. Comupt. Chem. 57 (2007) 385-392. | Zbl 1150.05012
[002] [3] R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory (Springer, New York, 2000). | Zbl 0938.05001
[003] [4] N.L. Biggs, Algebraic Graph Theory (Cambridge University Press, London, 1974). | Zbl 0284.05101
[004] [5] A.A. Dobrynin, R. Entringer and I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001) 211-249, doi: 10.1023/A:1010767517079. | Zbl 0982.05044
[005] [6] A.A. Dobrynin, I. Gutman, S. Klavžar and P. Zigert, Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002) 247-294, doi: 10.1023/A:1016290123303. | Zbl 0993.05059
[006] [7] P. Frankl and Z. Furedi, Extremal problems concerning Kneser graphs, J. Combin. Theory (B) 40 (1986) 270-284, doi: 10.1016/0095-8956(86)90084-5. | Zbl 0564.05002
[007] [8] I. Gutman and O. Polansky, Mathematical Concepts in Organic Chemistry (Springer-Verlag, Berlin, 1986). | Zbl 0657.92024
[008] [9] H. Hajabolhassan and X. Zhu, Circular chromatic number of Kneser graphs, J. Combin. Theory (B) 881 (2003) 299-303, doi: 10.1016/S0095-8956(03)00032-7. | Zbl 1025.05026
[009] [10] A. Johnson, F.C. Holroyd, and S. Stahl, Multichormatic numbers, star chromatic numbers and Kneser graphs, J. Graph Theory 26 (1997) 137-145, doi: 10.1002/(SICI)1097-0118(199711)26:3<137::AID-JGT4>3.0.CO;2-S | Zbl 0884.05041
[010] [11] K.W. Lih and D.F. Liu, Circular chromatic number of some reduced Kneser graphs, J. Graph Theory 41 (2002) 62-68, doi: 10.1002/jgt.10052. | Zbl 0996.05049
[011] [12] L. Lovasz, Kneser's conjecture, chromatic number and homotopy, J. Combin. Theory (A) 25 (1978) 319-324, doi: 10.1016/0097-3165(78)90022-5. | Zbl 0418.05028
[012] [13] M. Valencia-Pabon and J.-C. Vera, On the diameter of Kneser graphs, Discrete Math. 305 (2005) 383-385, doi: 10.1016/j.disc.2005.10.001. | Zbl 1100.05030
[013] [14] S.-P. Eu, B. Yang, and Y.-N Yeh, Generalised Wiener indices in hexagonal chains, Intl., J., Quantum Chem. 106 (2006) 426-435, doi: 10.1002/qua.20732.
[014] [15] S. Stahl, n-tuple coloring and associated graphs, J. Combin. Theory (B) 20 (1976) 185-203, doi: 10.1016/0095-8956(76)90010-1. | Zbl 0293.05115
[015] [16] S. Stahl, The multichromatic number of some Kneser graphs, Discrete Math. 185 (1998) 287-291, doi: 10.1016/S0012-365X(97)00211-2. | Zbl 0956.05045
[016] [17] K. Tilakam, Personal communication.
[017] [18] H. Wiener, Structural determination of Paraffin boiling points, J. Amer. Chem. Soc. 69 (1947) 17-20, doi: 10.1021/ja01193a005.
[018] [19] L. Xu and X. Guo, Catacondensed hexagonal systems with large Wiener numbers, MATCH Commun. Math. Comput. Chem. 55 (2006) 137-158. | Zbl 1088.05071