ArticleOriginal scientific text

Title

Wiener index of the tensor product of a path and a cycle

Authors 1, 1

Affiliations

  1. Department of Mathematics, Annamalai University, Annamalainagar 608 002, India

Abstract

The Wiener index, denoted by W(G), of a connected graph G is the sum of all pairwise distances of vertices of the graph, that is, W(G)=½Σu,vV(G)d(u,v). In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.

Keywords

tensor product, Wiener index

Bibliography

  1. R. Balakrishnan and K. Ranganathan, A Text Book of Graph Theory (Springer-Verlag, New York, 2000).
  2. R. Balakrishanan, N. Sridharan and K. Viswanathan Iyer, Wiener index of graphs with more than one cut vertex, Appl. Math. Lett. 21 (2008) 922-927, doi: 10.1016/j.aml.2007.10.003.
  3. Z. Du and B. Zhou, Minimum Wiener indices of trees and unicyclic graphs of given matching number, MATCH Commun. Math. Comput. Chem. 63 (2010) 101-112.
  4. Z. Du and B. Zhou, A note on Wiener indices of unicyclic graphs, Ars Combin. 93 (2009) 97-103.
  5. M. Fischermann, A. Hoffmann, D. Rautenbach and L. Volkmann, Wiener index versus maximum degree in trees, Discrete Appl. Math. 122 (2002) 127-137, doi: 10.1016/S0166-218X(01)00357-2.
  6. I. Gutman, S. Klavžar, Wiener number of vertex-weighted graphs and a chemical application, Discrete Appl. Math. 80 (1997) 73-81, doi: 10.1016/S0166-218X(97)00070-X.
  7. T.C. Hu, Optimum communication spanning trees, SIAM J. Comput. 3 (1974) 188-195, doi: 10.1137/0203015.
  8. W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (John Wiley, New York, 2000).
  9. F. Jelen and E. Triesch, Superdominance order and distance of trees with bounded maximum degree, Discrete Appl. Math. 125 (2003) 225-233, doi: 10.1016/S0166-218X(02)00195-6.
  10. K. Pattabiraman and P. Paulraja, Wiener index of the tensor product of cycles, submitted.
  11. P. Paulraja and N. Varadarajan, Independent sets and matchings in tensor product of graphs, Ars Combin. 72 (2004) 263-276.
  12. B.E. Sagan, Y.-N. Yeh and P. Zhang, The Wiener polynomial of a graph, manuscript.
Pages:
737-751
Main language of publication
English
Received
2010-07-01
Accepted
2010-11-09
Published
2011
Exact and natural sciences