图P_2×C_n 的均匀邻强边色数(英文)

ON THE EQUITABLE ADJACENT STRONG EDGE CHROMATICS NUMBER OF P_2×C_n

对图 G(V,E) ,一正常边染色 f 若满足 :(1)对 uv∈ E(G) ,f[u]≠ f[v],其中 f[u]={ f(uv) | uv∈E} ;(2 )对任意 i≠ j,有‖ Ei| - | Ej‖≤ 1,其中 Ei={ e| e∈ E(G)且 f(e) =i} .则称 f 为 G(V,E)的一 k-均匀邻强边染色 ,简称 k- EASC,并且称χ′eas(G) =min{ k|存在 G(V,E)的一 k- EASC为 G(V,E)的均匀邻强边色数。本文得到了图 P2 × Cn 的均匀邻强边色数。

Let G(V,E) be a simple connected graph with order not less than 3. A proper k edge coloring f of G(V,E) be called a k equitable adjacent strong edge coloring, be abbreviatted a k ASEC, of G(V,E) iff every uv∈E(G) have f≠f and ‖E i|-|E j‖≤1, where f={f(wx)|wx∈E(G)}, f(ux) is the color of edge wx∈E(G), and E k={e|e∈E(G) and f(e)=k}; and χ ′ eas (G) =min {k| there is a k EASEC of G} be called the equitable adjacent strong edge chromatics number of G(V,E). In this paper, we present some results about equitable adjacent strong edge chromatics number of graph P 2×C n.