Szeged index of bipartite unicyclic graphs

Document Type : Full Length Article

Authors

Department of Mathematics, South China Normal University Guangzhou 510631, P.R. China

Abstract

The Szeged index of a connected graph G is defined as the sum of products n1(e|G)n2(e|G) over all edges e = uv of G where n1(e|G) and n2(e|G) are respectively the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u In this paper, we determine the n-vertex bipartite unicyclic graphs with the first, the second, the third and the fourth smallest Szeged indices.

Graphical Abstract

Szeged index of bipartite unicyclic graphs

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References

References

[1] A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. Math. 66 (2001) 211-249.
[2] I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N. Y. 27 (1994) 9-15.
[3] B. Zhou, X.Cai, Z. Du, On Szeged indices of unicyclic graphs, MATCH Commun. Math. Comput. Chem. 63 (2010) 113-132.
[4] I. Gutman, L. Popović, P.V. Khadikar, S. Karmarkar, S. Joshi, M. Mandloi, Relations between Wiener and Szeged indices of monocyclic molecules, MATCH Commun. Math. Comput. Chem. 35 (1997) 91-103.
[5] B. Zhou, X. Cai, On detour index, MATCH Commun. Math. Comput. Chem. 63 (2010) 199-210.
Journal of Discrete Mathematics and Its Applications
Volume 1, 1-2
June 2011
Pages 13-24

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History

  • Receive Date: 10 January 2011
  • Revise Date: 10 February 2011
  • Accept Date: 13 March 2011
  • Publish Date: 01 June 2011

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