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 χ 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 χs&feet;(G) ≤ 2Δ(G) + 1 , where Δ( G) is the maximum degree of G. If, additionally, Δ(G) = 4, we prove χs&feet;( G) ≤ χs&feet;(T) + 2, where T is the characteristic tree of G.
|Commitee:||Brookfield, Gary, Fraser, Grant, Heubach, Silvia|
|School:||California State University, Los Angeles|
|School Location:||United States -- California|
|Source:||MAI 54/03M(E), Masters Abstracts International|
|Keywords:||Halin graph, Strong chromatic index|
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