@article{Luo2025, 
author = {Jianxin Luo and Jiangxu Kong},
title = {An upper bound for the semistrong chromatic index of Halin graphs},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {15811-15820},
keywords = {semistrong edge-coloring, semistrong chromatic index, Halin graph},
url = {https://www.sciopen.com/article/10.3934/math.2025708},
doi = {10.3934/math.2025708},
abstract = {For 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        χ          s      s              ′        (  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  ∪  C with maximum degree    Δ  (  G  ), the semistrong chromatic index satisfies        χ          s      s              ′        (  G  )  ≤  Δ  (  G  )  +  4, with equality attained by the wheel graphs        W    4   and        W    7  .}
}