| 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 chi s&feet;(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, Ne 4, and any wheel, then we prove chis&feet;(G) ≤ 2Delta(G) + 1 , where Delta( G) is the maximum degree of G. If, additionally, Delta(G) = 4, we prove chis&feet;( G) ≤ chis&feet;(T) + 2, where T is the characteristic tree of G.. |
