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《Journal of Qufu Normal University(Natural Science)》 2013-01
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D(β)-vertex Distinguishing Proper Total Coloring of Generalized Mycielski Graph M_n(P~3_m)

LIU Li-qun①,CHENG Xiang-en②(①College of Information and Mathematics,Yangtze University,434023,Jingzhou; ②College of Mathematics and Information Science,Northwest Normal University,730079,Lanzhou,Shaanxi,PRC)  
Let G be a simple graph,for any u,y∈V(G),d(u,v) denotes the distance between u and v.A proper total coloring of a graph G is called a D(β)-vertex distinguishing proper total coloring if for any two distinct vertices u,v∈V(G) with d(u,v)≤β,we have S(u)≠S(v).The D(β)-vertex distinguishing proper total chromatic number is the minimum number of colors required for an D(β)-vertex distinguishing proper total coloring of the graph G.In this paper,we obtained the D(β)-vertex distinguishing proper total chromatic number of generalized mycielski graph Mn(P3m).
【Fund】: 国家自然科学基金资助课题(61163037 61163054);; 西北师范大学“知识与科技创新工程”项目(nwnu-kjcxgc-03-61)
【CateGory Index】: O157.5
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1 YAN Qian-tai(School of Mathematics and Statistics,Anyang Normal University,Anyang 455002,China);On the general neighbor-distinguishing edge coloring of k-th power graphs[J];Journal of Anhui University(Natural Sciences Edition);2010-03
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