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Res."],"accepted":{"date-parts":[[2022,7,17]]},"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p>The spectral closeness of a graph <jats:italic>G<\/jats:italic> is defined as the spectral radius of the closeness matrix of <jats:italic>G<\/jats:italic>, whose (<jats:italic>u<\/jats:italic>,\u00a0<jats:italic>v<\/jats:italic>)-entry for vertex <jats:italic>u<\/jats:italic> and vertex <jats:italic>v<\/jats:italic> is 2<jats:sup>\u2212<jats:italic>d<\/jats:italic><jats:sub>G<\/jats:sub>(<jats:italic>u,v<\/jats:italic>)<\/jats:sup> if <jats:italic>u\u00a0\u2260\u00a0v<\/jats:italic> and 0 otherwise, where <jats:italic>d<\/jats:italic><jats:sub><jats:italic>G<\/jats:italic><\/jats:sub>(<jats:italic>u<\/jats:italic>,\u00a0<jats:italic>v<\/jats:italic>) is the distance between <jats:italic>u<\/jats:italic> and <jats:italic>v<\/jats:italic> in <jats:italic>G<\/jats:italic>. The residual spectral closeness of a nontrivial graph <jats:italic>G<\/jats:italic> is defined as the minimum spectral closeness of the subgraphs of <jats:italic>G<\/jats:italic> with one vertex deleted. We propose local grafting operations that decrease or increase the spectral closeness and determine those graphs that uniquely minimize and\/or maximize the spectral closeness in some families of graphs. We also discuss extremal properties of the residual spectral closeness.<\/jats:p>","DOI":"10.1051\/ro\/2022125","type":"journal-article","created":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T18:53:15Z","timestamp":1658343195000},"page":"2651-2668","source":"Crossref","is-referenced-by-count":7,"title":["On the spectral closeness and residual spectral closeness of graphs"],"prefix":"10.1051","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4019-8421","authenticated-orcid":false,"given":"Lu","family":"Zheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7321-9554","authenticated-orcid":false,"given":"Bo","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2022,8,18]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.laa.2014.06.010","volume":"458","author":"Aouchiche","year":"2014","journal-title":"Linear Algebra Appl."},{"key":"R2","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1142\/S0129054111008660","volume":"22","author":"Aytac","year":"2011","journal-title":"Internat. 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