• 제목/요약/키워드: Normalized Laplacian Estrada index

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THE NORMALIZED LAPLACIAN ESTRADA INDEX OF GRAPHS

  • Hakimi-Nezhaad, Mardjan;Hua, Hongbo;Ashrafi, Ali Reza;Qian, Shuhua
    • Journal of applied mathematics & informatics
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    • 제32권1_2호
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    • pp.227-245
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    • 2014
  • 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.