图C_5∨K_t的邻点可区别全色数  

Adjacent-Vertex-Distinguishing Total Chromatic Numbers of C_5∨K_t

作　　者：张芳红[1] 王治文[2] 陈祥恩[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070 [2]宁夏大学数学计算机学院,宁夏银川750021

出　　处：《数学的实践与认识》2012年第16期247-252,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61163037,61163054);宁夏自然基金(NZ1154);宁夏大学科学研究基金((E):ndzr10-7);西北师范大学“知识与科技创新工程”科研基金(nwnu-kjcxgc-03-61)

摘　　要：设f是图G的一个正常全染色.对任意x∈V(G),令C(x)表示与点x相关联的边的颜色以及点x的颜色所构成的集合.若对任意uv∈E(G),有C(u)≠C(v),则称.f是图G的一个邻点可区别全染色.对一个图G进行邻点可区别全染色所需的最少的颜色的数目称为G的邻点可区别全色数,记为Xat(G).用C_5∨K_t表示长为5的圈与t阶完全图的联图.讨论了C_5∨K_t的邻点可区别全色数.利用正多边形的对称性构造染色以及组合分析的方法,得到了当t是大于等于3的奇数以及t是偶数且2≤t≤22时,X_(at)(C_5 V K_t)=t+6,当t是偶数且t≥24时,X_(at)(C_5 V K_t)=t+7.Let f be a proper total coloring of G. For each x ∈ V（G）, let C（x） denote the set of all colors of the edhes incident with x and the color of x. If∨ uv ∈ E（G）, we have C（u） ≠ C（v）, then f is called an adjacent vertex distinguishing total coloring of G. The minimum number k for which there exists an adjacent vertex distinguishing total coloring of G using k colors is called the adjacent vertex distinguishing total chromatic number of G and denoted by XAt（G）. Let C5∨ Kt be the join of the cycle Ca of order 5 and the complete graph Kt of order t. In this paper, we discuss adjacent-vertex-distinguishing total chromatic numbers of C5 V Kt. By using symmetry of regular polygons to construct coloring, and methods of combinatorial analysis, we obtained that for t is odd with t ≥ 3 or t is even with 2 ≤ t ≤22, we have Xat（C5 ∨ Kt） = t ＋ 6; for t is even with t ≥ 24, we have Xat（C5 ∨ Kt） = t ＋ 7.

关 键 词：联图 全染色 邻点可区别全染色 邻点可区别全色数 

分 类 号：O157.5[理学—数学]