The strong edge-coloring of a graph G is to assign colors to all edges,so that the derived subgraphs of each color class are a matching.The minimum number of colors required in the strong edge-coloring of a graph G is called the strong chromatic index of the graph G,the degree of edge e=uv is recorded as d(e)=d(u)+d(v),the edge degree of G is recorded as d(G)=min { d(e)|e∈E(G)).}This paper proves that the strong chromatic index of the graph without K+1,3 with the maximum degree△ and edge degree of the graph greater than the number of vertices is at most △2-△+1.
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