@article{Bu2023, 
author = {Yuehua Bu and Qiang Yang and Junlei Zhu and Hongguo Zhu},
title = {Injective coloring of planar graphs with girth 5},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {17081-17090},
keywords = {injective coloring, planar graph, cycle},
url = {https://www.sciopen.com/article/10.3934/math.2023872},
doi = {10.3934/math.2023872},
abstract = {A    k-injective-coloring of a graph    G is a mapping    c  :    V      (    G    )    →      {          1      ,      2      ,      ⋯      ,      k        }   such that    c      (    u    )    ≠  c      (    v    )   for any two vertices    u and    v if    u and    v have a common vertex. The injective chromatic number of    G, denoted by              χ      i            (    G    )  , is the least    k such that    G has an injective k-coloring. In this paper, we prove that for planar graph    G with    g      (    G    )    ≥  5,    Δ      (    G    )    ≥  20 and without adjacent 5-cycles,              χ      i            (    G    )    ≤  Δ      (    G    )    +  2.}
}