Coloring the vertices of a particular graph has often been motivated by its utility to various applied fields and its mathematical interest. A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A dynamic k-coloring of a graph is a dynamic coloring with k colors. A dynamic k-coloring is also called a conditional (k, 2)-coloring. The smallest integer k such that G has a dynamic k-coloring is called the dynamic chromatic number \(\chi _d(G)\) of G. In this paper, we investigate the dynamic chromatic number for the line graph of sunlet graph and middle graph, total graph and central graph of sunlet graphs, paths and cycles. Also, we find the dynamic chromatic number for Mycielskian of paths and cycles and the join graph of paths and cycles.

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关于某些与周期相关的图的动态着色

为特定图形的顶点着色通常是由于其对各种应用领域的实用性及其数学兴趣而产生的。图G的动态着色是顶点集V（G）的适当着色，以使得对于度数的每个顶点至少为2，其邻点接收至少两种不同的颜色。图的动态k着色是具有k种颜色的动态着色。动态k色也称为条件（k，2）色。使得G具有动态k着色的最小整数k称为动态色数\（\ chi _d（G）\）的ģ。在本文中，我们研究了sunlet图和中间图的折线图，sunlet图的总图和中心图的动态色数，路径和周期。此外，我们找到路径和循环的Mycielskian的动态色数以及路径和循环的连接图。