广义Mycielski图的D(β)-点可区别VIE-全染色

D(β)-Vertex Distinguishing VIE-Total Coloring Of Generalized Mycielski Graph M_n(C_m^3)

单图G的D(β)-点可区VIE-全染色是满足当u,v∈V(G),0<d(u,v)≤β时,有S(u)≠S(v)的正常全染色,这里d(u,v)是任意两点u,v间的距离,S(u)是点u的色集合。D(β)-点可区别VIE-全色数是对图G进行D(β)-点可区别VIE-全染色所需最小色数。文中给出了当β=1,2时广义Mycielski图Mn(C3m)的D(β)-点可区别VIE-全色数。

Let G be a simple graph,A proper total coloring of G is called a D（β）-vertex distinguishing VIE-total coloring if for any two distinct vertices u,v∈V（G）,0〈d（u,v）≤β,we have S（u）≠S（v）,where d（u,v） denotes the distance between uand v for any u,v∈V（G）,S（u）is color set of the vertexu.The D（β）-vertex distinguishing VIE-total chromatic number is the minimum number of colors required for an D（β）-vertex distinguishing VIE-total coloring of G.In this paper,the D（β）-vertex distinguishing VIE-total chromatic number of generalized mycielski graph Mn（C3m） is discussed.