{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T00:22:53Z","timestamp":1720657373173},"reference-count":0,"publisher":"Combinatorial Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,6,30]]},"abstract":"<jats:p>We consider the eccentric graph of a graph  G , denoted by  e c c ( G ) , which has the same vertex set as  G , and two vertices in the eccentric graph are adjacent if and only if their distance in  G  is equal to the eccentricity of one of them. In this paper, we present a fundamental requirement for the isomorphism between  e c c ( G )  and the complement of  G , and show that the previous necessary condition given in the literature is inadequate. Also, we obtain that the diameter of  e c c ( T )  is at most 3 for any tree and get some characterizations of the eccentric graph of trees.<\/jats:p>","DOI":"10.61091\/ars159-09","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T05:14:41Z","timestamp":1720588481000},"page":"87-93","source":"Crossref","is-referenced-by-count":0,"title":["On the Eccentric Graph of Trees"],"prefix":"10.61091","volume":"159","author":[{"given":"Sezer","family":"Sorgun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, Nevsehir Haci Bektacs Veli University, Nevsehir 50300, Turkey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Esma","family":"Elyemani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, Nevsehir Haci Bektacs Veli University, Nevsehir 50300, Turkey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2024,6,30]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T05:14:49Z","timestamp":1720588489000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-159\/on-the-eccentric-graph-of-trees\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,6,30]]},"published-print":{"date-parts":[[2024,6,30]]}},"URL":"https:\/\/doi.org\/10.61091\/ars159-09","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,30]]}}}