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The quotient between the largest and the second smallest normalized Laplacian matrix eigenvalues of a connected graph, is called the normalized Laplacian spectral ratio. Some bounds of the normalized Laplacian spectral ratio of a connected graph are considered. In the paper, we improve a relation of the normalized Laplacian spectral ratio of regular graphs, and we obtain the effects on the normalized Laplacian spectral ratio of a graph by the Operations. <\/jats:p>","DOI":"10.1142\/s0129626425300016","type":"journal-article","created":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T09:18:37Z","timestamp":1739524717000},"source":"Crossref","is-referenced-by-count":0,"title":["Normalized Laplacian Spectral Ratio of Graphs"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-2182-3055","authenticated-orcid":false,"given":"Min","family":"Cai","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-8132-2196","authenticated-orcid":false,"given":"JiaJia","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1148-056X","authenticated-orcid":false,"given":"Shumin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, China"}]}],"member":"219","published-online":{"date-parts":[[2025,2,14]]},"reference":[{"volume-title":"Spectral Graph Theory","year":"1997","author":"Chung F.","key":"S0129626425300016BIB001"},{"key":"S0129626425300016BIB004","first-page":"63","volume":"4","author":"Dragomir S. 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