On the adjacent vertex-distinguishing total chromatic numbers of the graphs with Δ (G) = 3
On the adjacent vertex-distinguishing total chromatic numbers of the graphs with Δ (G) = 3
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DOI：
10.1007/s10878-006-9038-0
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发表时间：
2007-01
影响因子：
1
通讯作者：
Haiying Wang
中科院分区：
文献类型：
--
作者：
Haiying Wang
设 是一个简单图，T(G) 是 G 的顶点和边的集合。让C成为ak颜色集。 G 的（适当）总谈话着色是一个函数，使得 T(G) 的相邻或关联元素都不会接收到相同的颜色。对于任何一个，表示。 Gi 的总着色 f 称为任意边的相邻顶点区分。而最小的颜色数称为相邻顶点可区分的总色数G。在本文中，我们证明了对于所有最大度数为三的连通图。这是朝着相邻顶点区分总着色的猜想迈出的一步。
Letbe a simple graph andT(G) be the set of vertices and edges ofG. LetCbe ak-color set. A (proper) totalk-coloringfofGis a functionsuch that no adjacent or incident elements ofT(G) receive the same color. For any, denote. The totalk-coloringfofGis called the adjacent vertex-distinguishing iffor any edge. And the smallest number of colors is called the adjacent vertex-distinguishing total chromatic numberofG. In this paper, we prove thatfor all connected graphs with maximum degree three. This is a step towards a conjecture on the adjacent vertex-distinguishing total coloring.