{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T02:03:02Z","timestamp":1773885782603,"version":"3.50.1"},"reference-count":16,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T00:00:00Z","timestamp":1617667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005357","name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja","doi-asserted-by":"publisher","award":["APVV-19-0153"],"award-info":[{"award-number":["APVV-19-0153"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006109","name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","doi-asserted-by":"publisher","award":["VEGA 1\/0233\/18"],"award-info":[{"award-number":["VEGA 1\/0233\/18"]}],"id":[{"id":"10.13039\/501100006109","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling \u03c6:E(G)\u2192{1,2,\u2026,k} of positive integers to the edges of G is called irregular if the weights of the vertices, defined as wt\u03c6(v)=\u2211u\u2208N(v)\u03c6(uv), are all different. The irregularity strength of a graph G is known as the maximal integer k, minimized over all irregular labelings, and is set to \u221e if no such labeling exists. In this paper, we determine the exact value of the irregularity strength and the modular irregularity strength of fan graphs.<\/jats:p>","DOI":"10.3390\/sym13040605","type":"journal-article","created":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T03:58:31Z","timestamp":1617681511000},"page":"605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["The Irregularity and Modular Irregularity Strength of Fan Graphs"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5758-0347","authenticated-orcid":false,"given":"Martin","family":"Ba\u010da","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Informatics, Technical University, 042 00 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1366-440X","authenticated-orcid":false,"given":"Zuzana","family":"Kim\u00e1kov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Informatics, Technical University, 042 00 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7968-960X","authenticated-orcid":false,"given":"Marcela","family":"Lascs\u00e1kov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Informatics, Technical University, 042 00 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8432-9836","authenticated-orcid":false,"given":"Andrea","family":"Semani\u010dov\u00e1-Fe\u0148ov\u010d\u00edkov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Informatics, Technical University, 042 00 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1002\/jgt.10056","article-title":"On graph irregularity strength","volume":"41","author":"Frieze","year":"2002","journal-title":"J. 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