On Generalized Distance Gaussian Estrada Index of Graphs

Alhevaz, Abdollah, Baghipur, Maryam and Shang, Yilun (2019) On Generalized Distance Gaussian Estrada Index of Graphs. Symmetry, 11 (10). ISSN 2073-8994

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Official URL: https://www.mdpi.com/2073-8994/11/10/1276

Abstract

For a simple undirected connected graph G of order n, let D(G) , DL(G) , DQ(G) and Tr(G) be, respectively, the distance matrix, the distance Laplacian matrix, the distance signless Laplacian matrix and the diagonal matrix of the vertex transmissions of G. The generalized distance matrix Dα(G) is signified by Dα(G)=αTr(G)+(1−α)D(G) , where α∈[0,1]. Here, we propose a new kind of Estrada index based on the Gaussianization of the generalized distance matrix of a graph. Let ∂1,∂2,…,∂n be the generalized distance eigenvalues of a graph G. We define the generalized distance Gaussian Estrada index Pα(G) , as Pα(G)=∑ni=1e−∂2i. Since characterization of Pα(G) is very appealing in quantum information theory, it is interesting to study the quantity Pα(G) and explore some properties like the bounds, the dependence on the graph topology G and the dependence on the parameter α . In this paper, we establish some bounds for the generalized distance Gaussian Estrada index Pα(G) of a connected graph G, involving the different graph parameters, including the order n, the Wiener index W(G) , the transmission degrees and the parameter α∈[0,1] , and characterize the extremal graphs attaining these bounds.

Item Type: Article
Uncontrolled Keywords: Gaussian Estrada index, generalized distance matrix (spectrum), Wiener index, generalized distance Gaussian Estrada index, transmission regular graph
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Paul Burns
Date Deposited: 11 Oct 2019 14:22
Last Modified: 11 Oct 2019 14:30
URI: http://nrl.northumbria.ac.uk/id/eprint/41087

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