{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:03:11Z","timestamp":1777366991322,"version":"3.51.4"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,30]],"date-time":"2021-01-30T00:00:00Z","timestamp":1611964800000},"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\/501100003194","name":"Agent\u00fara Ministerstva \u0160kolstva, Vedy, V\u00fdskumu a \u0160portu SR","doi-asserted-by":"publisher","award":["VEGA 1\/0233\/18"],"award-info":[{"award-number":["VEGA 1\/0233\/18"]}],"id":[{"id":"10.13039\/501100003194","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Graph labeling is the mapping of elements of a graph (which can be vertices, edges, faces or a combination) to a set of numbers. The mapping usually produces partial sums (weights) of the labeled elements of the graph, and they often have an asymmetrical distribution. In this paper, we study vertex\u2013face and edge\u2013face labelings of two-connected plane graphs. We introduce two new graph characteristics, namely the vertex\u2013face H-irregularity strength and edge\u2013face H-irregularity strength of plane graphs. Estimations of these characteristics are obtained, and exact values for two families of graphs are determined.<\/jats:p>","DOI":"10.3390\/sym13020229","type":"journal-article","created":{"date-parts":[[2021,1,30]],"date-time":"2021-01-30T06:22:20Z","timestamp":1611987740000},"page":"229","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["H-Irregularity Strengths of Plane 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\/0000-0002-9894-061X","authenticated-orcid":false,"given":"Nurdin","family":"Hinding","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Natural Sciences, Hasanuddin University, Makassar 90245, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aisha","family":"Javed","sequence":"additional","affiliation":[{"name":"Abdus Salam School of Mathematical Sciences, GC University, Lahore 54000, Pakistan"}],"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":[[2021,1,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chartrand, G., Lesniak, L., and Zhang, P. (2016). Graphs & Digraphs, Taylor & Francis Group. [6th ed.].","DOI":"10.1201\/b19731"},{"key":"ref_2","first-page":"187","article-title":"Irregular networks","volume":"64","author":"Chartrand","year":"1988","journal-title":"Congr. Numer."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1137\/0403038","article-title":"Irregular assignments of trees and forests","volume":"3","author":"Aigner","year":"1990","journal-title":"SIAM J. Discret. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/S0895480196314291","article-title":"A tight bound on the irregularity strength of graphs","volume":"13","author":"Nierhoff","year":"2000","journal-title":"SIAM J. Discret. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1002\/jgt.20313","article-title":"Irregularity strength of dense graphs","volume":"58","author":"Cuckler","year":"2008","journal-title":"J. Graph Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1137\/070707385","article-title":"Linear bound on the irregularity strength and the total vertex irregularity strength of graphs","volume":"23","year":"2009","journal-title":"SIAM J. Discret. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1137\/090774112","article-title":"A new upper bound for the irregularity strength of graphs","volume":"25","author":"Kalkowski","year":"2011","journal-title":"SIAM J. Discret. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1137\/120886650","article-title":"On the irregularity strength of dense graphs","volume":"28","author":"Majerski","year":"2014","journal-title":"SIAM J. Discret. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/S0012-365X(98)00112-5","article-title":"Irregularity strength of trees","volume":"190","author":"Amar","year":"1998","journal-title":"Discrete Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3461","DOI":"10.1016\/j.disc.2012.06.017","article-title":"Irregular labellings of Circulant graphs","volume":"312","author":"Anholcer","year":"2012","journal-title":"Discrete Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1002\/jgt.10158","article-title":"On the irregularity strength of trees","volume":"45","author":"Bohman","year":"2004","journal-title":"J. Graph Theory"},{"key":"ref_12","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. Graph Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1650070","DOI":"10.1142\/S1793830916500701","article-title":"On vertex and edge H-irregularity strengths of graphs","volume":"8","author":"Ashraf","year":"2016","journal-title":"Discrete Math. Algorithms Appl."},{"key":"ref_14","first-page":"263","article-title":"On the face irregularity strength","volume":"9","author":"Kathiresan","year":"2015","journal-title":"Appl. Math. Inf. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/229\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:17:28Z","timestamp":1760159848000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/229"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,30]]},"references-count":14,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["sym13020229"],"URL":"https:\/\/doi.org\/10.3390\/sym13020229","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,30]]}}}