{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:35:20Z","timestamp":1757619320215,"version":"3.44.0"},"reference-count":7,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T00:00:00Z","timestamp":1753574400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T00:00:00Z","timestamp":1753574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100008899","name":"University of South Carolina","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100008899","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In 1971, Graham and Pollak provided a formula for the determinant of the distance matrix of any tree on <jats:italic>n<\/jats:italic> vertices. Yan and Yeh reproved this by exploiting the fact that pendant vertices can be deleted from trees without changing the remaining entries of the distance matrix. Considering failures of their argument to generalize invites the question: which graphs have the property that deleting any one vertex results in a change to some pairwise distance? Such worst-case graphs are known as \u201cdistance critical\u201d, and were first studied by Erd\u0151s and Howorka. This work explores the structural properties of distance critical graphs, preservation of distance-criticality by products, and the nature of extremal distance critical graphs. We end with a few open questions.<\/jats:p>","DOI":"10.1007\/s00373-025-02943-4","type":"journal-article","created":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T15:39:57Z","timestamp":1753630797000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distance Critical Graphs"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5187-1322","authenticated-orcid":false,"given":"Joshua","family":"Cooper","sequence":"first","affiliation":[]},{"given":"Gabrielle","family":"Tauscheck","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"2943_CR1","doi-asserted-by":"publisher","first-page":"2495","DOI":"10.1002\/j.1538-7305.1971.tb02618.x","volume":"50","author":"RL Graham","year":"1971","unstructured":"Graham, R.L., Pollak, H.O.: On the addressing problem for loop switching. Bell Syst. Tech. 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The On-Line Encyclopedia of Integer Sequences, Published electronically at (2024) https:\/\/oeis.org"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-02943-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-025-02943-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-02943-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T17:49:34Z","timestamp":1757267374000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-025-02943-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,27]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["2943"],"URL":"https:\/\/doi.org\/10.1007\/s00373-025-02943-4","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2025,7,27]]},"assertion":[{"value":"16 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"87"}}