@article{Hu2026, 
author = {Xingxing Hu and Yunfang Tang},
title = {The star edge coloring of cubic Halin graphs with star chromatic index    5},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {3132-3141},
keywords = {star chromatic index, caterpillar, complete tree, Halin graph},
url = {https://www.sciopen.com/article/10.3934/math.2026124},
doi = {10.3934/math.2026124},
abstract = {The star chromatic index of a graph    G, denoted by        χ          s      t        ′    (  G  ), is the minimum number of colors needed to properly color the edges of    G such that no path or cycle of length four is bi-colored. Casselgren et al. and Hou et al. independently proved that the star chromatic index of a cubic Halin graph, except in the case of a special graph, is at most    6. It remains an open problem to determine which of such graphs have star chromatic index    5. In this paper, we show that if    G  ≠      N                  e        2             is a cubic Halin graph whose tree is a caterpillar or a complete tree, then        χ          s      t        ′    (  G  )  =  5.}
}