ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 31(4) (2011) 737-751
DOI: 10.7151/dmgt.1576

Wiener Index of the Tensor Product
of a Path and a Cycle

K. Pattabiraman and P. Paulraja

Department of Mathematics
Annamalai University
Annamalainagar 608 002, India


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) = ½ Σu,v ∈ V(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

2010 Mathematics Subject Classification: 05C12, 05C76.


[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.

Received 1 July 2010
Revised 9 November 2010
Accepted 11 November 2010