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An upper bound for the semistrong chromatic index of Halin graphs

dc.contributor.authorJianxin Luo
dc.contributor.authorJiangxu Kong
dc.contributor.otherSchool of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
dc.contributor.otherSchool of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
dc.date.accessioned2025-08-27T02:32:32Z
dc.date.accessioned2025-10-08T08:04:29Z
dc.date.available2025-10-08T08:04:29Z
dc.date.issued2025-07
dc.identifier.urihttps://www.aimspress.com/article/doi/10.3934/math.2025708
dc.identifier.urihttp://digilib.fisipol.ugm.ac.id/repo/handle/15717717/35587
dc.description.abstractFor a graph $ G $, a semistrong matching is a matching $ M $ such that every edge in $ M $ contains at least one endpoint of degree one in the induced subgraph $ G[V(M)] $. The semistrong chromatic index $ \chi_{s s}^{\prime}(G) $ denotes the minimum number of colors required for a proper edge-coloring where each color class induces a semistrong matching. We study this parameter for Halin graphs, which are planar graphs formed by connecting all leaves of a tree $ T $ (with no degree-two vertices) via an outer cycle $ C $. Our main result establishes that for any Halin graph $ G = T\cup C $ with maximum degree $ \Delta(G) $, the semistrong chromatic index satisfies $ \chi_{s s}^{\prime}(G) \leq \Delta(G)+4 $, with equality attained by the wheel graphs $ W_4 $ and $ W_7 $.
dc.language.isoEN
dc.publisherAIMS Press
dc.subject.lccMathematics
dc.titleAn upper bound for the semistrong chromatic index of Halin graphs
dc.typeArticle
dc.description.keywordssemistrong edge-coloring
dc.description.keywordssemistrong chromatic index
dc.description.keywordshalin graph
dc.description.pages15811-15820
dc.description.doi10.3934/math.2025708
dc.title.journalAIMS Mathematics
dc.identifier.e-issn2473-6988
dc.identifier.oaifedc73bbab344320a78cf5d441a1e46e
dc.journal.infoVolume 10, Issue 7


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