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 using π(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 H is no more than π(H)+1. In addition, if p ≤ 3, the specific coloring method is given by using π(H) colors. Consequently, we show that the vertex distinguishing edge chromatic number of H is π(H)+1 at most