On The Adjacent Strong Edge Coloring of 1-Tree
Zhang Zhong-fu · Journal of Mathematical Research and Exposition · 2000
Let G(V,E) be a graph. A k -proper edge coloring f is called a k -adjacent strong edge coloring of G(V,E) iff every uv∈ E(G) satisfies f[u] ≠ f[v], where f[u] = (f(uw) |uw∈E(G) }, is called k -ASEC for short, and X_(as)~'(G) = min{k | There exists a k-ASEC of G} is called the adjacent strong edge chromatic number of G. In this paper,we present a conjec- ture that for 2-connected graph G(V,E) (G(V,E) ≠ C_5 ),△ (G) ≤X_(as)~'(G) ≤ △(G) + 2, and prove that for 1-tree graph with△(G)≥4 have△(G) ≤ X_(as)~'(G) ≤ △(G) + 1 and X_(as)~'(G)= △(G) + 1 iff E(G[V_△]) ≠( , where V_△＝ {u|u∈ V(G), d(u) =△(G)}.