{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T13:41:20Z","timestamp":1765806080263,"version":"3.41.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"the National Science Foundation of China","award":["12061059"],"award-info":[{"award-number":["12061059"]}]},{"name":"the Qinghai Key Laboratory of Internet of Things Project","award":["2017-ZJ-Y21"],"award-info":[{"award-number":["2017-ZJ-Y21"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:p> For a vertex set [Formula: see text], we say that [Formula: see text] is a monitoring-edge-geodetic set (MEG-set for short) of graph [Formula: see text], that is, some vertices of [Formula: see text] can monitor an edge of the graph, if and only if we can remove that edge would change the distance between some pair of vertices in the set. The monitoring-edge-geodetic number [Formula: see text] of a graph [Formula: see text] is defined as the minimum cardinality of a monitoring-edge-geodetic set of [Formula: see text]. The line graph [Formula: see text] of [Formula: see text] is the graph whose vertices are in one-to-one correspondence with the edges of [Formula: see text], that is, if two vertices are adjacent in [Formula: see text] if and only if the corresponding edges have a common vertex in [Formula: see text]. In this paper, we study the relation between [Formula: see text] and [Formula: see text], and prove that [Formula: see text]. Next, we have determined the exact values for a MEG-set of some special graphs and their line graphs. For a graph [Formula: see text] and its line graph [Formula: see text], we prove that [Formula: see text] can be arbitrarily large. <\/jats:p>","DOI":"10.1142\/s0219265923500251","type":"journal-article","created":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T10:22:35Z","timestamp":1697970155000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Monitoring-Edge-Geodetic Numbers of Line Graphs"],"prefix":"10.1142","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-7058-4909","authenticated-orcid":false,"given":"Gemaji","family":"Bao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2523-7090","authenticated-orcid":false,"given":"Chenxu","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining, Qinghai 810008, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-5041-3733","authenticated-orcid":false,"given":"Zhiqiang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4006-7456","authenticated-orcid":false,"given":"Zhen","family":"Ji","sequence":"additional","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining, Qinghai 810008, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-1254-7246","authenticated-orcid":false,"given":"Xin","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0896-6922","authenticated-orcid":false,"given":"Peiyao","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2023,10,20]]},"reference":[{"issue":"2","key":"S0219265923500251BIB001","first-page":"146","volume":"2","author":"Akbar A.","year":"2010","journal-title":"J. Math. Research"},{"issue":"4","key":"S0219265923500251BIB002","first-page":"37","volume":"2","author":"Alireza A.","year":"2013","journal-title":"Trans. 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