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Title: Extremal graphs for Estrada indices
Author: Andrade, Enide
Lenes, Eber
Mallea-Zepeda, Exequiel
Robbiano, María
Rodríguez Z., Jonnathan
Keywords: Estrada index
Signless Laplacian Estrada index
Laplacian Estrada index
Chromatic number
Vertex connectivity
Edge connectivity
Line graph
Issue Date: 1-Mar-2020
Publisher: Elsevier
Abstract: Let $\mathcal{G}$ be a simple undirected connected graph. The signless Laplacian Estrada, Laplacian Estrada and Estrada indices of a graph $\mathcal{G}$ is the sum of the exponentials of the signless Laplacian eigenvalues, Laplacian eigenvalues and eigenvalues of $\mathcal{G}$, respectively. The present work derives an upper bound for the Estrada index of a graph as a function of its chromatic number, in the family of graphs whose color classes have order not less than a fixed positive integer. The graphs for which the upper bound is tight is obtained. Additionally, an upper bound for the Estrada Index of the complement of a graph in the previous family of graphs with two color classes is given. A Nordhaus-Gaddum type inequality for the Laplacian Estrada index when {$\mathcal{G}$ is a bipartite} graph with color classes of order not less than $2$, is presented. Moreover, a sharp upper bound for the Estrada index of the line graph and for the signless Laplacian index of a graph in terms of connectivity is obtained.
Peer review: yes
DOI: 10.1016/j.laa.2019.10.029
ISSN: 0024-3795
Appears in Collections:CIDMA - Artigos
DMat - Artigos
OGTCG - Artigos

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