两类特殊的k重Mycielski图的邻点强可区别E-全染色

Adaject Vertex Strong Distinguishing E-total Coloring of Two Special Classes of K-multi-Mycielski Graphs

对简单图G,如果图G存在一个染色法f,使得任意两个相邻的顶点染不同的颜色,任意一条边与其关联的点染不同的颜色,任意两个相邻点的色集合不同,其中每个点的色集合包含该点及其关联边和相邻点的颜色,则称该染色法f为G的邻点强可区别E-全染色,且称所用最小的颜色数为图G的邻点强可区别E-全色数。本文应用反证法和构造染色函数法研究了路和圈的距离为3的k重Mycielski图的邻点强可区别E-全染色,并得出了其邻点强可区别E-全色数。

Let be a single graph. A total coloring of called adjacent vertex strongly distinguishing E-total coloring, if no two adjacent vertex of receive the same color and no edge with incident vertex assigned the same color, and for any two adjacent vertexes and , there must be where is a set of color of the vertex, including the color of the edge of the vertex and the color of the vertex agjacent to the ver- tex. The minimal number of colors required for the adjacent vertex strongly distinguishing E-total coloring of is called the adjacent ver- tex distinguishing E-total chromatic numbers. In this paper, the adjacent vertex strongly distinguishing E-total coloring of distance with three K-muhi-Mycielski Graphs of path and circle are given by contradiction and constructing colorable function. Meanwhile, the adja- cent vertex strongly distinguishing E-total chromatic of them are obtained.