منابع مشابه
A note on the Laplacian Estrada index of trees
Abstract The Laplacian Estrada index of a graphG is defined as LEE(G) = ∑n i=1 e μi , where μ1 ≥ μ2 ≥ · · · ≥ μn−1 ≥ μn = 0 are the eigenvalues of its Laplacian matrix. An unsolved problem in [19] is whether Sn(3, n − 3) or Cn(n − 5) has the third maximal Laplacian Estrada index among all trees on n vertices, where Sn(3, n − 3) is the double tree formed by adding an edge between the centers of ...
متن کاملLower Bounds for Estrada Index
If G is an (n,m)-graph whose spectrum consists of the numbers λ1, λ2, . . . , λn, then its Estrada index is EE(G) = ∑n i=1 e λi . We establish lower bounds for EE(G) in terms of n and m. Introduction In this paper we are concerned with simple graphs, that have no loops and no multiple or directed edges. Let G be such a graph, and let n and m be the number of its vertices and edges. Then we say ...
متن کاملEstrada Index of Benzenoid Hydrocarbons
A structure-descriptor EE, recently proposed by Estrada, is examined. If λ1, λ2, . . . ,λn are the eigenvalues of the molecular graph, then EE = n ∑ i=1 eλi . In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a1 n cosh (√ 2m/n ) +a2, where a1 ≈ 1.098 and a2 =−0.64 are empirically determined fitt...
متن کاملOn the Estrada index of cacti
Let G be a simple connected graph on n vertices and λ1, λ2, . . . , λn be the eigenvalues of the adjacency matrix of G. The Estrada index of G is defined as EE(G) = Σ i=1 ei . A cactus is a connected graph in which any two cycles have at most one common vertex. In this work, the unique graph with maximal Estrada index in the class of all cacti with n vertices and k cycles was determined. Also, ...
متن کاملBounds of distance Estrada index of graphs
Let λ1, λ2, · · · , λn be the eigenvalues of the distance matrix of a connected graph G. The distance Estrada index of G is defined as DEE(G) = ∑ n i=1 ei . In this note, we present new lower and upper bounds for DEE(G). In addition, a Nordhaus-Gaddum type inequality for DEE(G) is given. MSC 2010: 05C12, 15A42.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.08.025