图C_5∨K_t的邻点可区别全色数

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.

Adjacent-Vertex-Distinguishing Total Chromatic Numbers of C5 ∨ Kt

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 X_(at)(G). Let C_5∨K_t be the join of the cycle Cs of order 5 and the complete graph K_t of order t.In this paper,we discuss adjacent-vertex-distinguishing total chromatic numbers of C_5 V K_t.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 haveχ_(at)(C_5∨K_t)=t+6; for t is even with t≥24,we haveχ_(at)(C_5∨K_t)=t+7.