T型六角系统的点可区别边染色

Vertex Distinguishing Proper Edge Coloring of T-Shaped Hexagonal Systems

根据T-型六角系统链H结构的性质以及2度点的排列特点,用π(H)+1种颜色给出了p(≥4)阶H中2度点的点可区别边染色算法,紧接着分析其3度点的染色特点,通过调整个别边的颜色,最终证明H(p≥4)的点可区别色数不超过π(H)+1.另外,当p≤3时,用π(H)种颜色给出具体的点可区别边染色方法,从而证明H的点可区别边色数不超过π(H)+1.

In this paper,according to the properties of the T-shaped hexagonal system H and the arrangement of its 2-degree vertices,we give an algorithm of vertex-distinguishing proper edge coloring of 2-degree vertices on H（p≥4）by usingπ（H）＋1 colors.Then we analyze the color sets of its vertices with degree 3,and the color of some edges incident with those vertices are adjusted.Finally,we obtain that if p≥4,the vertex distinguishing edge chromatic number of His no more thanπ（H）＋1.In addition,if p≤3,the specific coloring method is given by usingπ（H）colors.Consequently,we show that the vertex distinguishing edge chromatic number of Hisπ（H）＋1 at most.