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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Lower Bounds of the Resolvent Estrada Indices for Line Graphs and Complementary Graphs

Discontinuity, Nonlinearity, and Complexity 11(1) (2022) 49--55 | DOI:10.5890/DNC.2022.03.004

Shuxiang Jia$^{1}$, Bo Deng$^{1,2,3,4}$ , Chengfu Ye$^{1}$, Weilin Liang$^{1}$

$^1$ School of Mathematics and Statistics, Qinghai Normal University, Xining, 810001, China

$^2$ Academy of Plateau, Science and Sustainability, Xining, Qinghai 810008, China

$^3$ Key Laboratory of Tibetan Information Processing, Ministry of Education, Qinghai Province, China

$^4$ Tibetan Intelligent Information Processing and Machine Translation Key Laboratory, Qinghai, 810008, China

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Abstract

Let $G$ be a simple graph of order $n$. The resolvent Estrada index of $G$ is defined as $REE(G)=\sum_{i=1}^n {\frac{n-1}{n-1-\lambda _i }} $, where $\lambda _1 , \lambda _2 , \cdots , \lambda _n $ are the eigenvalues of the adjacency matrix $A(G)$. In this paper, we present several lower bounds of the resolvent Estrada indices for line graphs of any regular graphs and their complementary graphs.

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