JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 92-96.doi: 10.6040/j.issn.1671-9352.0.2019.510

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Description of the upper(lower)bounds of Resolvent Estrada index

JIA Shu-xiang1, DENG Bo1,2,3,4*, YE Cheng-fu1, FU Feng1, CHEN Hui-long1   

  1. 1. College of Mathematics and Statistics, Qinghai Normal University, Xining 810008, Qinghai, China;
    2. Tibetan Intelligent Information Processing and Machine Translation Key Laboratory, Xining 810008, Qinghai, China;
    3. Key Laboratory of Tibetan Information Processing and Machine Translation, Qinghai Province, Xining 810008, Qinghai, China;
    4. College of Science, Guangdong University of Petrochemical Technology, Maoming 525000, Guangdong, China
  • Published:2020-04-09

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Abstract: The Resolvent Estrada index in graph G is the topological index of a class of important graphs proposed by Estrada and Higham in 2010 to detect the centrality of complex networks and molecular structures. It is defined as follow.REE(G)=∑ni=1((n-1)/(n-1-λi))=∑ni=1(1-(λ1)/(n-1))-1,where λ1,λ2,…,λn are the eigenvalues of the adjacency matrix of G. REE(G)is often used to quantify the degree of molecular chains so that it is widely used in the filed of the quantum chemistry. In this paper, Cauchy-Schwartz inequality and Resolvent Estrada energy are used to describe the upper and lower bounds of Resolvent Estrada index.

Key words: Resolvent Estrada index, Resolvent Estrada energy, adjacent matrix, eigenvalue

CLC Number: 

  • O157
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