{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T00:55:27Z","timestamp":1778547327125,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T00:00:00Z","timestamp":1717113600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2024,5,31]]},"abstract":"<jats:p>Foucaud et al. recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. Given a graph G = ( V( G), E( G)), a set M \u2286 V( G) is a distance-edge-monitoring set if for every edge e \u2208 E( G), there is a vertex x \u2208 M and a vertex y \u2208 V( G) such that the edge e belongs to all shortest paths between x and y. The smallest size of such a set in G is denoted by dem( G). Denoted by G \u2013 e (resp. G\\ u) the subgraph of G obtained by removing the edge e from G (resp. a vertex u together with all its incident edges from G). In this paper, we first show that dem( G \u2013 e) \u2013 dem( G) \u2264 2 for any graph G and edge e \u2208 E( G). Moreover, the bound is sharp. Next, we construct two graphs G and H to show that dem( G) \u2013 dem( G\\ u) and dem( H \\ v) \u2013 dem( H) can be arbitrarily large, where u \u2208 V( G) and v \u2208 V( H). We also study the relation between dem( H) and dem( G), where H is a subgraph of G. In the end, we give an algorithm to judge whether the distance-edge-monitoring set still remain in the resulting graph when any edge of a graph G is deleted.<\/jats:p>","DOI":"10.3233\/fi-242176","type":"journal-article","created":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T10:54:26Z","timestamp":1717152866000},"page":"141-163","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Perturbation Results for Distance-edge-monitoring Numbers"],"prefix":"10.1177","volume":"191","author":[{"given":"Chenxu","family":"Yang","sequence":"first","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining, Qinghai 810008, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ralf","family":"Klasing","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Bordeaux, Bordeaux INP, CNRS, LaBRI, UMR 5800, Talence, France."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changxiang","family":"He","sequence":"additional","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaping","family":"Mao","sequence":"additional","affiliation":[{"name":"Academy of Plateau Science and Sustainabilit and School of Mathematics and Statistics, Xining, Qinghai 810008, China."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,5,31]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-242176","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-242176","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:59Z","timestamp":1777444379000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-242176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,31]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,5,31]]}},"alternative-id":["10.3233\/FI-242176"],"URL":"https:\/\/doi.org\/10.3233\/fi-242176","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,31]]}}}