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http://hdl.handle.net/10773/27207
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 |
URI: | http://hdl.handle.net/10773/27207 |
DOI: | 10.1016/j.laa.2019.10.029 |
ISSN: | 0024-3795 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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EStrada indices.pdf | 317.94 kB | Adobe PDF | View/Open |
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