{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:24:45Z","timestamp":1753885485606,"version":"3.41.2"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12031018","12201569"],"award-info":[{"award-number":["12031018","12201569"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,7]]},"abstract":"<jats:p> A [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] is a mapping [Formula: see text] such that [Formula: see text] for any three consecutive edges [Formula: see text],[Formula: see text],[Formula: see text] of a path or a [Formula: see text]-cycle. [Formula: see text][Formula: see text] has a [Formula: see text]-injective-edge-coloring[Formula: see text] is called the injective chromatic index of G. In this paper, we prove that for planar graphs [Formula: see text] with [Formula: see text], (1)[Formula: see text] if [Formula: see text]; (2)[Formula: see text] if [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830923500507","type":"journal-article","created":{"date-parts":[[2023,5,20]],"date-time":"2023-05-20T05:28:25Z","timestamp":1684560505000},"source":"Crossref","is-referenced-by-count":0,"title":["Injective-edge-coloring of planar graphs with girth restriction"],"prefix":"10.1142","volume":"16","author":[{"given":"Yuehua","family":"Bu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, P. R. China"},{"name":"Department of Basics, Zhejiang Guangsha Vocational and Technical, University of Construction, Zhejiang 322100, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongguo","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,8,5]]},"reference":[{"key":"S1793830923500507BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830918500222"},{"key":"S1793830923500507BIB003","first-page":"675","volume":"49","author":"Bu Y. H.","year":"2020","journal-title":"Adv. Math. (China)"},{"key":"S1793830923500507BIB004","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1919411C"},{"key":"S1793830923500507BIB005","series-title":"Congressus Numerantium","first-page":"125","volume-title":"Proc. West Coast Conf. Combinatorics Graph Theory and Computing","author":"Erd\u0151s P.","year":"1979"},{"key":"S1793830923500507BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2021.106121"},{"key":"S1793830923500507BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2021.103355"},{"key":"S1793830923500507BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-022-02562-3"},{"key":"S1793830923500507BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2021.07.010"},{"key":"S1793830923500507BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2021.12.021"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830923500507","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T03:31:04Z","timestamp":1715139064000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830923500507"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,5]]},"references-count":9,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["10.1142\/S1793830923500507"],"URL":"https:\/\/doi.org\/10.1142\/s1793830923500507","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2023,8,5]]},"article-number":"2350050"}}