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A proper edge coloring of a graph G is called star edge coloring if there is no bi-colored path or cycle of length four in G. The minimum number of colors needed to star color the edges of G is called the star chromatic index of G, denoted by χs′(G). In 2013[1], Dvoˇr´ak et. al. proved that for a subcubic graph G, χs′ (G) ≤ 7 and conjectured that it is less than or equal to 6. In this paper, we show that if a subcubic graph G has maximum average degree less than 83 then χs′(G) ≤ 6.

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