若干联图的点可区别均匀边色数

k-正常边染色法f,若满足任两个不同点的关联边色集不同,则称f为G的k-点可区别边染色,简记为k-VDEC of G,并称最小的k为G的点可区别边色数;对k-VDEC若再满足任意两色的边数之差不超过1,则称f为G的点可区别均匀边染色,简记为k-VDEEC of G,并称最小的k为G的点可区别均匀边色数．本文得到了图等阶的路和路,路和圈,圈和圈的联图的点可区别均匀边色数．

On the Vertex-Distinguishing-Equitable Edge Chromatic Number of Some Join-Graphs

A k-proper edge coloring of a simple graph G is called vertex-distinguishing edge coloring of G if for any two distinct vertices u and v in G, the set of colors assigned to the edges incident to u differs from the set of colors assigned to the edges incident to v, is abbreviated k-VDEC, the minimal number k of colors required for vertex-distinguishing edge coloring of G is called the vertex-distinguishing edge chromatic number of G, is denoted by x′υd(G). For a k-VDEC of G, it satisfied with the difference for any two sets of colors included the edges not more than 1 also, it is called k-vertex-distinguishing-equitable edge coloring of G, abbreviated to k-VDEEC. And the minimal number k is called the vertex-distinguishing-equitable edge chromatic number of G, denoted by x′υde(G). In this paper, we obtain the vertex-distinguishing-equitable edge chromatic numbers of join-graphs of path and path, path and cycle, cycle and cycle with equivalent order.