On revised szeged spectrum of a graph

Article Sidebar

PDF
Published: Dec 30, 2014
DOI: https://doi.org/10.5556/j.tkjm.45.2014.1463
Keywords:
Revised Szeged Spectrum eigenvalue

Main Article Content

Nader Habibi
Ali Reza Ashrafi

Abstract

The revised Szeged index is a molecular structure descriptor equal to the sum of products $[n_u(e) + \frac{n_0(e)}{2}][n_v(e) + \frac{n_0(e)}{2}]$ over all edges $e = uv$ of the molecular graph $G$, where $n_0(e)$ is the number of vertices equidistant from $u$ and $v$, $n_u(e)$ is the number of vertices closer to $u$ than $v$ and $n_v(e)$ is defined analogously. The adjacency matrix of a graph weighted in this way is called its revised Szeged matrix and the set of its eigenvalues is the revised Szeged spectrum of $G$. In this paper some new results on the revised Szeged spectrum of graphs are presented.

Article Details

How to Cite
Habibi, N., & Ashrafi, A. R. (2014). On revised szeged spectrum of a graph. Tamkang Journal of Mathematics, 45(4), 375–387. https://doi.org/10.5556/j.tkjm.45.2014.1463
Issue
Vol. 45 No. 4 (2014)
Section
Papers
Author Biographies

Nader Habibi

Department ofMathematics, University of Zanjan, Zanjan, I. R. Iran.

Ali Reza Ashrafi

Department of Pure Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan 87317- 51167, I. R. Iran.

References

N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1974.

D. M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs, Academic Press, New York, 1980.

M. Faghani and A. R. Ashrafi, Revised and edge revised Szeged indices of graphs, Ars Math. Contemporanea, (2014), 153--160.

G. H. Fath-Tabar, T. Dov slic and A. R. Ashrafi, On the Szeged and the Laplacian Szeged spectrum of a graph, Linear Algebra Appl., 433(2010), 662--671.

C. Godsil and G. Royle, Algebraic Graph Theory, Springer-Verlag, New York, 2001.

I. Gutman, P. V. Khadikar and T. Khaddar, Wiener and Szeged indices of benzenoid hydrocarbons containing a linear polyacene fragment, MATCH Commun. Math. Comput. Chem., 35 (1997), 105--116.

I. Gutman, L. Popovi$ acutec$, P.V. Khadikar, S. Karmarkar, S. Joshi and M. Mandloi,Relations between Wiener and Szeged indices of monocyclic molecules, MATCH Commun. Math. Comput. Chem., 35(1997), 91--103.

I. Gutman, A formula for the Wiener number of trees and its extension to the graphs containing cycles, Graph Theory Notes Ney York, 17(1994), 9--15.

W. Imrich and S. Klavzar, Produt Graphs: Structure and Recognition, John Wiley & Sons, New York, USA, 2000.

J. Jerebic, S. Klavzar and D. F. Rall, Distance-Balanced Graphs, Annals of Combinatorics, 12(2008), 71--79.

M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi, A matrix method for computing Szeged and PI indices of Join and composition of graphs, Linear Algebra Appl., 429

(2008), 2702--2708.

T. Pisanski and M. Randic, Use of the Szeged index and the revised Szeged index for measuring network bipartivity, Discrete Appl. Math.,158(2010), 1936--1944.

T. Pisanski and J.v Zerovnik, Edge-contributions of some topological indices and arboreality of molecular graphs, Ars Math. Contemporanea, (2009), 49--58.

M. Randic, On generalization of Wiener index to cyclic structures, Acta Chim. Slov., 49 (2002), 483--496.

H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc., 69, (1947) 17--20.

R. Xing and B. Zhou, On the revised Szeged index, Discrete Appl. Math.159(2011), 69--78.