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http://dx.doi.org/10.14317/jami.2014.227

THE NORMALIZED LAPLACIAN ESTRADA INDEX OF GRAPHS  

Hakimi-Nezhaad, Mardjan (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan)
Hua, Hongbo (Department of Mathematics, Nanjing University, Faculty of Mathematics and Physics, Huaiyin Institute of Technology)
Ashrafi, Ali Reza (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan)
Qian, Shuhua (Faculty of Mathematics and Physics, Huaiyin Institute of Technology)
Publication Information
Journal of applied mathematics & informatics / v.32, no.1_2, 2014 , pp. 227-245 More about this Journal
Abstract
Suppose G is a simple graph. The ${\ell}$-eigenvalues ${\delta}_1$, ${\delta}_2$,..., ${\delta}_n$ of G are the eigenvalues of its normalized Laplacian ${\ell}$. The normalized Laplacian Estrada index of the graph G is dened as ${\ell}EE$ = ${\ell}EE$(G) = ${\sum}^n_{i=1}e^{{\delta}_i}$. In this paper the basic properties of ${\ell}EE$ are investigated. Moreover, some lower and upper bounds for the normalized Laplacian Estrada index in terms of the number of vertices, edges and the Randic index are obtained. In addition, some relations between ${\ell}EE$ and graph energy $E_{\ell}$(G) are presented.
Keywords
Normalized Laplacian energy; Normalized Laplacian Estrada index; Estrada index; Randic index;
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