{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T01:09:36Z","timestamp":1773104976103,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971274"],"award-info":[{"award-number":["11971274"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p> The eccentricity matrix [Formula: see text] of a graph [Formula: see text] is constructed from the distance matrix by keeping each row and each column only the largest distances with [Formula: see text] where [Formula: see text] is the distance between two vertices [Formula: see text] and [Formula: see text], and [Formula: see text] is the eccentricity of the vertex [Formula: see text]. The [Formula: see text]-eigenvalues of [Formula: see text] are those of its eccentricity matrix. In this paper, employing the well-known Cauchy Interlacing Theorem we give the following lower bounds for the second, the third and the fourth largest [Formula: see text]-eigenvalues by means of the diameter [Formula: see text] of [Formula: see text]: [Formula: see text] where [Formula: see text] is the second largest root of [Formula: see text]. Moreover, we further discuss the graphs achieving the above lower bounds. <\/jats:p>","DOI":"10.1142\/s1793830922501828","type":"journal-article","created":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T11:34:37Z","timestamp":1668598477000},"source":"Crossref","is-referenced-by-count":4,"title":["The diameter and eccentricity eigenvalues of graphs"],"prefix":"10.1142","volume":"16","author":[{"given":"Yunzhe","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, P. R. 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