Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/27207
 Title: Extremal graphs for Estrada indices Author: Andrade, EnideLenes, EberMallea-Zepeda, ExequielRobbiano, MaríaRodríguez Z., Jonnathan Keywords: Estrada indexSignless Laplacian Estrada indexLaplacian Estrada indexChromatic numberVertex connectivityEdge connectivityLine 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 - ArtigosDMat - ArtigosOGTCG - Artigos

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