{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:06:04Z","timestamp":1760241964384,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,4]],"date-time":"2018-11-04T00:00:00Z","timestamp":1541289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The geodetic number of a graph is an important graph invariant. In 2002, Atici showed the geodetic set determination of a graph is an NP-Complete problem. In this paper, we compute the geodetic set and geodetic number of an important class of graphs called the k-th power of a cycle. This class of graphs has various applications in Computer Networks design and Distributed computing. The k-th power of a cycle is the graph that has the same set of vertices as the cycle and two different vertices in the k-th power of this cycle are adjacent if the distance between them is at most k.<\/jats:p>","DOI":"10.3390\/sym10110592","type":"journal-article","created":{"date-parts":[[2018,11,5]],"date-time":"2018-11-05T10:43:45Z","timestamp":1541414625000},"page":"592","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Geodetic Number of Powers of Cycles"],"prefix":"10.3390","volume":"10","author":[{"given":"Mohammad","family":"Abudayah","sequence":"first","affiliation":[{"name":"School of Basic Sciences and Humanities, German Jordanian University, Amman 11180, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1145-0256","authenticated-orcid":false,"given":"Omar","family":"Alomari","sequence":"additional","affiliation":[{"name":"School of Basic Sciences and Humanities, German Jordanian University, Amman 11180, Jordan"}]},{"given":"Hassan","family":"Al Ezeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Jordan, Amman 11942, Jordan"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,4]]},"reference":[{"key":"ref_1","first-page":"525","article-title":"The geodetic number of a graph","volume":"16","author":"Kim","year":"2004","journal-title":"J. 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