The strong chromatic index of Halin graphs

The Strong Chromatic Index of Halin Graphs By Ziyu Hu A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they have adjacent endpoints. The strong chromatic index of a graph G, denoted by χs(G), is the minimum number of colors needed for a strong edge coloring of G. A Halin graph G is a planar graph constructed by connecting all leaves of a characteristic tree T without vertices of degree two through a cycle. If a Halin graph G is different from Ne2, Ne4, and any wheel, then we prove χs(G) 6 2∆(G) + 1 , where ∆(G) is the maximum degree of G. If, additionally, ∆(G) = 4, we prove χs(G) 6 χ ′ s(T ) + 2, where T is the characteristic tree of G.