一类4-正则平面图的邻点可区别关联色数

The Adjacent Vertex Distinguishing Incidence Coloring Numbers of a Class of 4-Regular Planar Graphs

所谓图R_n是指具有如下结构的平面图:R_n=(V,E),其中顶点集合V={u_1,u_2,…,u_n}U{v_1,v_2,…,v_n},边集合E={u_iu_(i+1),v_iv_(i+1),u_iv_i,u_iv_(i+1)|i=1,2,…,n},其中u_(n+1)=u_1,v_(n+1)=v_1.通过研究R_n的邻点可区别关联着色,给出了当n=4,n是3或者5的正整数倍时,R_n的邻点可区别关联色数.

The graph Rn is defined byRn = （V, E）, V={u1,u2,…,un）∪{v1,V2,…,vn） and E = {uiui＋1,vivi＋1,uivi,uivi＋1│i=1,2,…,n）}, where un＋1 = u1, vn＋l = v1. By studying the adjacent vertex distinguishing incidence coloring of Rn, we determine the adjacent vertex distinguishing incidence coloring numbers of them, when n = 4, n = 3k or n = 5k （ k is a positive integer）.