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On the Estrada and Laplacian Estrada indices of graphs

On the Estrada and Laplacian Estrada indices of graphs,10.1016/j.laa.2011.03.057,Linear Algebra and Its Applications,Zhibin Du,Zhongzhu Liu

On the Estrada and Laplacian Estrada indices of graphs   (Citations: 1)
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The Estrada index of a graph G is defined as EE(G)=∑i=1neλi, where λ1,λ2,…,λn are the eigenvalues of G. The Laplacian Estrada index of a graph G is defined as LEE(G)=∑i=1neμi, where μ1,μ2,…,μn are the Laplacian eigenvalues of G. An edge grafting operation on a graph moves a pendent edge between two pendent paths. We study the change of Estrada index of graph under edge grafting operation between two pendent paths at two adjacent vertices. As the application, we give the result on the change of Laplacian Estrada index of bipartite graph under edge grafting operation between two pendent paths at the same vertex. We also determine the unique tree with minimum Laplacian Estrada index among the set of trees with given maximum degree, and the unique trees with maximum Laplacian Estrada indices among the set of trees with given diameter, number of pendent vertices, matching number, independence number and domination number, respectively.
Journal: Linear Algebra and Its Applications - LINEAR ALGEBRA APPL , vol. 435, no. 8, pp. 2065-2076, 2011
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