The Tight Bound for the Strong Chromatic Indices of Claw-Free Subcubic Graphs

Let G be a graph and k positive integer. A strong k-edge-coloring of is mapping $$\phi : E(G)\rightarrow \{1,2,\dots ,k\}$$ such that for any two edges e $$e'$$ are either adjacent to each other or common edge, (e)\ne \phi (e')$$ . The chromatic index G, denoted as $$\chi '_{s}(G)$$ , the minimum integer has k-edge-coloring. Lv, Li Zhang [Graphs Combinatorics 38 (3) (2022) 63] proved if claw-free subcubic than triangular prism then _s'(G)\le 8$$ In addition, they asked upper bound 8 can improved 7. this paper, we answer question in affirmative. Our proof implies polynomial-time algorithm finding 7-edge-colorings graphs. We also construct infinitely many graphs with their indices attaining