The strong chromatic index of graphs with edge weight eight

The edge weight of a graph G is defined to be $$\max \{d_G(u) + d_G(v): uv \in E(G)\}$$ max { d G ( u ) + d G ( v ) : u v ∈ E ( G ) } . The strong chromatic index of a graph is the minimum value of k such that the edge set of G can be partitioned into k induced matchings. In this article, we prove that the strong chromatic index of a graph with edge weight eight is at most 21.