Deniz, Zakir2024-08-232024-08-2320241382-69051573-2886https://doi.org/10.1007/s10878-024-01169-zhttps://hdl.handle.net/20.500.12684/14508A vertex coloring of a graph G is called a 2-distance coloring if any two vertices at distance at most 2 from each other receive different colors. Suppose that G is a planar graph with girth 5 and maximum degree Delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}. We prove that G admits a 2-distance Delta+7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta +7$$\end{document} coloring, which improves the result of Dong and Lin (J Comb Optim 32(2):645-655, 2016). Moreover, we prove that G admits a 2-distance Delta+6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta +6$$\end{document} coloring when Delta >= 10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \ge 10$$\end{document}.en10.1007/s10878-024-01169-zinfo:eu-repo/semantics/closedAccessColoring2-distance coloringGirthPlanar graphSquareArticle4742-s2.0-85192065768WOS:001214226300002Q2N/A