Edge Cover Coloring Of Several Planar Graphs

Let G(V, E)be a simple graph,C is a mapping from E to a color set {1,2,...,k} that is X:Eâ†'{1,2,...,k),it is called a k-edge-coloring of G.Let Cv-1(i)denote the number of edges of G incident with vertex Ï… receiving color i by the coloring C. C is called a k-edge cover-coloring of G if CÏ…-1(i)≥1for each υ∈V,i∈{1,2,...,k).The maximum positive integeor for which a k-edge cover-coloring of G exists is called the edge cover chromatic index of G, it is denoted by X’c:(G). It is known that δ-1≤x’c:(G)≤δ.G is a graph of class CI if x’c:(G)=δ(G);otherwise G is a graph of class CII. In this paper, we consider the classification of2-boundary planar graph based on the edge cover chromatic index and obtain a necessary and suffcient condition for boundary uncrossed2-boundary planar graph to be of class CI:let G be a boundary uncrossed2-boundary planar graph and9(G)≥3,G is class CI if and only if δ(G)[｜V(G)|/2]≤|E(G)|ï¼› and discuss the edge cover-coloring of planar graph with girth constraint.