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

K. Pattabiraman; P. Paulraja

Discussiones Mathematicae Graph Theory (2011)

  • Volume: 31, Issue: 4, page 737-751
  • ISSN: 2083-5892

Abstract

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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 Σ u , v ∈ V ( G ) d ( u , v ) . In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.

How to cite

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K. Pattabiraman, and P. Paulraja. "Wiener index of the tensor product of a path and a cycle." Discussiones Mathematicae Graph Theory 31.4 (2011): 737-751. <http://eudml.org/doc/271031>.

@article{K2011,
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, $W(G) = ½Σ_\{u,v ∈ V(G)\} d(u,v)$. In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.},
author = {K. Pattabiraman, P. Paulraja},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {tensor product; Wiener index},
language = {eng},
number = {4},
pages = {737-751},
title = {Wiener index of the tensor product of a path and a cycle},
url = {http://eudml.org/doc/271031},
volume = {31},
year = {2011},
}

TY - JOUR
AU - K. Pattabiraman
AU - P. Paulraja
TI - Wiener index of the tensor product of a path and a cycle
JO - Discussiones Mathematicae Graph Theory
PY - 2011
VL - 31
IS - 4
SP - 737
EP - 751
AB - 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, $W(G) = ½Σ_{u,v ∈ V(G)} d(u,v)$. In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.
LA - eng
KW - tensor product; Wiener index
UR - http://eudml.org/doc/271031
ER -

References

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  3. [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. Zbl1299.05083
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  7. [7] T.C. Hu, Optimum communication spanning trees, SIAM J. Comput. 3 (1974) 188-195, doi: 10.1137/0203015. Zbl0269.90010
  8. [8] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (John Wiley, New York, 2000). 
  9. [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. Zbl1009.05052
  10. [10] K. Pattabiraman and P. Paulraja, Wiener index of the tensor product of cycles, submitted. Zbl1255.05065
  11. [11] P. Paulraja and N. Varadarajan, Independent sets and matchings in tensor product of graphs, Ars Combin. 72 (2004) 263-276. Zbl1075.05069
  12. [12] B.E. Sagan, Y.-N. Yeh and P. Zhang, The Wiener polynomial of a graph, manuscript. 

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