{"title":"Estrada index of dynamic random graphs","authors":"Yi-lun Shang","doi":"10.1007/s11766-023-3727-7","DOIUrl":null,"url":null,"abstract":"<div><p>The Estrada index of a graph <i>G</i> on <i>n</i> vertices is defined by <span>\\(EE(G) = \\sum\\nolimits_{i = 1}^n {{e^{{\\lambda _i}}}} \\)</span>, where <i>λ</i><sub>1</sub>, <i>λ</i><sub>2</sub>, ⋯, <i>λ</i><sub><i>n</i></sub> are the adjacency eigenvalues of <i>G</i>. We define two general types of dynamic graphs evolving according to continuous-time Markov processes with their stationary distributions matching the Erdös-Rényi random graph and the random graph with given expected degrees, respectively. We formulate some new estimates and upper and lower bounds for the Estrada indices of these dynamic graphs.</p></div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"38 2","pages":"159 - 165"},"PeriodicalIF":1.0000,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11766-023-3727-7.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-023-3727-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
The Estrada index of a graph G on n vertices is defined by \(EE(G) = \sum\nolimits_{i = 1}^n {{e^{{\lambda _i}}}} \), where λ1, λ2, ⋯, λn are the adjacency eigenvalues of G. We define two general types of dynamic graphs evolving according to continuous-time Markov processes with their stationary distributions matching the Erdös-Rényi random graph and the random graph with given expected degrees, respectively. We formulate some new estimates and upper and lower bounds for the Estrada indices of these dynamic graphs.
期刊介绍：
Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects.
The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry.
Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.
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