On the Adjacent Strong Edge Coloring of Outer Plane Graphs

Abstract:

      A k-adjacent strong edge coloring of graph G(V, E) is defined as a proper kedge coloring f of graph G(V, E) such that f[u] ≠ f[v] for every uv ∈ E(G), where f[u] ={f(uw)|uw ∈ E(G)} and f(uw) denotes the color of uw, and the adjacent strong edge chromatic number is defined as x′_as(G) = min{k| there is a k-adjacent strong edge coloring of G}. In this paper, it has been proved that △≤ x′_as(G) ≤△ + 1 for outer plane graphs with △(G) ≥ 5, and x′_as(G) = △ + 1 if and only if there exist adjacent vertices with maximum degree.