The Wiener number of Kneser graphs

Rangaswami Balakrishnan; S. Francis Raj

Discussiones Mathematicae Graph Theory (2008)

  • Volume: 28, Issue: 2, page 219-228
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Rangaswami Balakrishnan, and S. Francis Raj. "The Wiener number of Kneser graphs." Discussiones Mathematicae Graph Theory 28.2 (2008): 219-228. <http://eudml.org/doc/270235>.

@article{RangaswamiBalakrishnan2008,
abstract = {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.},
author = {Rangaswami Balakrishnan, S. Francis Raj},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Wiener number; Kneser graph; odd graph},
language = {eng},
number = {2},
pages = {219-228},
title = {The Wiener number of Kneser graphs},
url = {http://eudml.org/doc/270235},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Rangaswami Balakrishnan
AU - S. Francis Raj
TI - The Wiener number of Kneser graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 2
SP - 219
EP - 228
AB - 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.
LA - eng
KW - Wiener number; Kneser graph; odd graph
UR - http://eudml.org/doc/270235
ER -

References

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  1. [1] R. Balakrishanan, N. Sridharan and K. Viswanathan, The Wiener index of odd graphs, Indian Inst. Sci. 86 (2006) 527-531. Zbl1226.05105
  2. [2] R. Balakrishanan, K. Viswanathan and K.T. Raghavendra, Wiener index of two special trees, MATCH Commun. Math. Comupt. Chem. 57 (2007) 385-392. Zbl1150.05012
  3. [3] R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory (Springer, New York, 2000). Zbl0938.05001
  4. [4] N.L. Biggs, Algebraic Graph Theory (Cambridge University Press, London, 1974). Zbl0284.05101
  5. [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. Zbl0982.05044
  6. [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. Zbl0993.05059
  7. [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. Zbl0564.05002
  8. [8] I. Gutman and O. Polansky, Mathematical Concepts in Organic Chemistry (Springer-Verlag, Berlin, 1986). Zbl0657.92024
  9. [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. Zbl1025.05026
  10. [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 Zbl0884.05041
  11. [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. Zbl0996.05049
  12. [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. Zbl0418.05028
  13. [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. Zbl1100.05030
  14. [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. 
  15. [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. Zbl0293.05115
  16. [16] S. Stahl, The multichromatic number of some Kneser graphs, Discrete Math. 185 (1998) 287-291, doi: 10.1016/S0012-365X(97)00211-2. Zbl0956.05045
  17. [17] K. Tilakam, Personal communication. 
  18. [18] H. Wiener, Structural determination of Paraffin boiling points, J. Amer. Chem. Soc. 69 (1947) 17-20, doi: 10.1021/ja01193a005. 
  19. [19] L. Xu and X. Guo, Catacondensed hexagonal systems with large Wiener numbers, MATCH Commun. Math. Comput. Chem. 55 (2006) 137-158. Zbl1088.05071

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