Journal ArticleDOI
Distance Estrada index of random graphs
TLDR
In this paper, lower and upper bounds for the distance Estrada index of a simple graph were established for almost all graphs, and the eigenvalues of its distance matrix were derived.Abstract:
Suppose is a simple graph and are the eigenvalues of its distance matrix . The distance Estrada index of is defined as the sum of , . In this paper, we establish better lower and upper bounds to for almost all graphs .read more
Citations
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Proceedings ArticleDOI
Random graphs
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Journal ArticleDOI
Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.
TL;DR: It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.
Journal ArticleDOI
On the Generalized Distance Energy of Graphs
TL;DR: In this article, the generalized distance matrix of a simple connected graph G is defined as a convex combination of the convex combinations of T r (G ) + (1 − α ) D (G) for 0 ≤ α ≤ 1.
Journal ArticleDOI
Classification of renewable sources of electricity in the context of sustainable development of the new EU member states
TL;DR: In this article, the authors employed hierarchical cluster analysis in an attempt to distinguish those countries among the new EU Member States that increased their electrical capacity from renewable energy sources to the greatest extent while paying attention to their energy intensity.
Journal ArticleDOI
Merging the Spectral Theories of Distance Estrada and Distance Signless Laplacian Estrada Indices of Graphs
TL;DR: In this paper, the generalized distance Estrada index of a graph G is defined as a generalized distance matrix D α (G ) = ∑ i = 1 n e ∂ i − 2 α W ( G ) n, where W denotes the Wiener index of G.
References
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Journal ArticleDOI
On the Estrada index conjecture
Kinkar Ch. Das,Sang-Gu Lee +1 more
TL;DR: Pena et al. as discussed by the authors proved that the star S n has maximum Estrada index for any tree of order n, and that the path P n has minimum index for either tree or connected graph.
Journal ArticleDOI
Inverse of the distance matrix of a block graph
TL;DR: In this article, the determinant and the inverse of a block graph are derived, and a formula for both determinants and inverse, D − 1 of D, is given, where D is the distance matrix.
Estrada Index of Random Graphs
Zhi Chen,Yi-Zheng Fan +1 more
TL;DR: In this article, the Estrada index of a graph G of order n is defined as EE(G )= � n=1 e λ i, where λ 1,λ 2,...,λ n are the eigenvalues of the graph G. By the limiting behavior of the spectrum of random symmetric matrices, the authors formulate an exact estimate to EE (G )f or almost all graphs G, and establish a lower bound and an upper bound for almost all multipartite graphs G.
Various energies of random graphs 1
Wenxue Du,Xueliang Li,Yiyang Li +2 more
TL;DR: In this paper, a tight bound of LE + (G) for almost all graphs by probabilistic and algebraic approaches has been established for Lapacian-energy-like invariants.
Journal Article
On the Distance Estrada Index of Graphs
A.D. Güngör,S.B. Bozkurt +1 more
TL;DR: In this article, the distance Estrada index of a connected graph G is defined and investigated as DEE = DEE(G) = n P i = 1 e µi.