外平面图的邻点可辨别边染色.pdf

 Æ  G(V,E ) G ϕx ∈ V(G) x S ϕ(x). Æ G x ,y S ϕ(x) S ϕ(y ) ϕ G nd . 4 Æ ℄ 3. : i NEIGHBOUR-DISTINGUISHING EDGE CHROMATIC NUMBER ON OURTER PLANE GRAPH ABSTRACT Let G(V,E ) be a graph, for an edge-colouring ϕ of graph G, the colour set of a vertex x ∈ V(G) is the set of colours of edges incident to x , and will be de- noted by S ϕ(x). If S ϕ(x) S ϕ(y ) for every two adjacent vertices x ,y , we call this edge colouring ϕneighbour-distinguishing edge colouring . In short, it’s calledndedge-colouring. In this paper, according to the structure character- istics of the outer plane graph, we can make the upper bound of the neighbour- distinguishing edge chromatic number of the 2-connected outer plane graph reach to 4. Furthermore, we get the conclusion that 2-connected outer plane graph can ndedge-coloured using 3 colours, by analyzing thendedge-colouring of be some particular 2-connected outer plane graphs such as 2-connected outer plane graph without triangle , 2-connected outer plane graph which dual graph is a tree and so on. KEY WORDS: neighbour-distinguishingplane graphouter plane graphedge colouring ii 1. |S |—— . 2. V(G)—— G . 3. E (G)—— G . 4. ν(G)—— G . 5. ǫ(G)—— G . 6. ∆(G)—— G . 7. δ(G)—— G . 8. G H—— G H . 9. (X ,Y)—— G ℄. 10. Kn,n—— . 11. dG (v)—— G v . ∗ G . 12.G —— 13.P