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, . In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1576, author = {K. Pattabiraman and P. Paulraja}, title = {Wiener index of the tensor product of a path and a cycle}, journal = {Discussiones Mathematicae Graph Theory}, volume = {31}, year = {2011}, pages = {737-751}, zbl = {1255.05065}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1576} }
K. Pattabiraman; P. Paulraja. Wiener index of the tensor product of a path and a cycle. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 737-751. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1576/
[000] [1] R. Balakrishnan and K. Ranganathan, A Text Book of Graph Theory (Springer-Verlag, New York, 2000). | Zbl 0938.05001
[001] [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. | Zbl 1152.05322
[002] [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. | Zbl 1299.05083
[003] [4] Z. Du and B. Zhou, A note on Wiener indices of unicyclic graphs, Ars Combin. 93 (2009) 97-103. | Zbl 1224.05139
[004] [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. | Zbl 0993.05061
[005] [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. | Zbl 0889.05046
[006] [7] T.C. Hu, Optimum communication spanning trees, SIAM J. Comput. 3 (1974) 188-195, doi: 10.1137/0203015. | Zbl 0269.90010
[007] [8] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (John Wiley, New York, 2000).
[008] [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. | Zbl 1009.05052
[009] [10] K. Pattabiraman and P. Paulraja, Wiener index of the tensor product of cycles, submitted. | Zbl 1255.05065
[010] [11] P. Paulraja and N. Varadarajan, Independent sets and matchings in tensor product of graphs, Ars Combin. 72 (2004) 263-276. | Zbl 1075.05069
[011] [12] B.E. Sagan, Y.-N. Yeh and P. Zhang, The Wiener polynomial of a graph, manuscript.