{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:57:35Z","timestamp":1760237855773,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T00:00:00Z","timestamp":1660089600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11801494","11971196"],"award-info":[{"award-number":["11801494","11971196"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let G be a graph and \u03c3:E(G)\u2192{+1,\u22121} be a mapping. The pair (G,\u03c3), denoted by G\u03c3, is called a signed graph. A (proper) l-edge coloring \u03b3 of G\u03c3 is a mapping from each vertex\u2013edge incidence of G\u03c3 to Mq such that \u03b3(v,e)=\u2212\u03c3(e)\u03b3(w,e) for each edge e=vw, and no two vertex\u2013edge incidences have the same color; that is, \u03b3(v,e)\u2260\u03b3(v,f). The chromatic index is the minimal number q such that G\u03c3 has a proper q-edge coloring, denoted by \u03c7\u2032(G\u03c3). In 2020, Behr proved that the chromatic index of a signed graph is its maximum degree or maximum plus one. In this paper, we considered the chromatic index of the signed generalized Petersen graph GP(n,2) and show that its chromatic index is its maximum degree for most cases. In detail, we proved that (1) \u03c7\u2032(GP\u03c3(n,2))=3 if n\u22613 mod 6(n\u22659); (2) \u03c7\u2032(GP\u03c3(n,2))=3 if n=2p(p\u22654).<\/jats:p>","DOI":"10.3390\/axioms11080393","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T09:42:56Z","timestamp":1660124576000},"page":"393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Chromatic Index of the Signed Generalized Petersen Graph GP(n,2)"],"prefix":"10.3390","volume":"11","author":[{"given":"Shanshan","family":"Zheng","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Yangzhou University, Yangzhou 225002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongyan","family":"Cai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanpei","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8990-9610","authenticated-orcid":false,"given":"Qiang","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Yangzhou University, Yangzhou 225002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/S0012-365X(03)00138-9","article-title":"The Petersen graph is not 3-edge-colorable\u2014A new proof","volume":"268","author":"Naserasr","year":"2003","journal-title":"Discret. 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Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.ipl.2013.03.017","article-title":"Edge coloring total k-labeling of generalized Petersen graphs","volume":"113","author":"Khennoufa","year":"2013","journal-title":"Inf. Process. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chen, M., Miao, L., and Zhou, S. (2020). Strong Edge Coloring of Generalized Petersen Graphs. Mathematics, 8.","DOI":"10.3390\/math8081265"},{"key":"ref_16","first-page":"7279","article-title":"Injective edge coloring of generalized Petersen graphs","volume":"6","author":"Li","year":"2021","journal-title":"AIMS Math."},{"key":"ref_17","first-page":"431","article-title":"Strong edge chromatic index of the generalized Petersen graphs","volume":"321","author":"Yang","year":"2008","journal-title":"Appl. Math. 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On the forcing spectrum of generalized Petersen graph P(n, 2). arXiv."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/393\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:06:43Z","timestamp":1760141203000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/393"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,10]]},"references-count":20,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["axioms11080393"],"URL":"https:\/\/doi.org\/10.3390\/axioms11080393","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,8,10]]}}}