【作者】 田京京；

【导师】 刘信生；

【作者基本信息】 西北师范大学 ， 应用数学， 2007， 硕士

【摘要】 张忠辅等人在[49]提出了图的D（β）-点可区别边染色的概念,本文通过概率方法和具体构造染色的方法研究了D（β）-点可区别的边染色。本文有四部分构成。第一部分主要是引如一些在本文所需要的基本概念与预备知识。第二部分讨论了D（β）-点可区别边染色的性质,给出了路和圈的D（3）-点可区别边色数,并归纳总结P_n,C_n,S_n,K_n,F_n,W_n的D（β）-点可区别边色数。第三部分通过具体构造染色的方法讨论并给出了联图S_m∨P_n∨P_n,F_m∨P_n的D（β）-点可区别的边色数。第四部分通过具体构造染色的方法讨论并给出了β=1,2,3时五类冠图C_m·P_n,C_m·S_n,C_m·C_n,C_m·F_n,C_m·W_n的D（β）点可区别边色数。第五部分先应用Lovasz局部引理的一般形式,讨论并得到了对最大度为d的简单图G,有X’_2-vd（G）≤32d²,d＞4,X’_3-vd（G）≤8d^5/2,d≥6.以及β≥4,d≥4时,D（β）-点可区别的边色数的上界。即（?）,然后,用得到了D（2）-点可区别的边色数的另一个上界,有（?）,则（?）。更多还原

【Abstract】 In 2006,Zhang Zhongfu present a new concept of the D（β）-vertex-distinguishing proper edge-coloring and conjecture,see[8].In this pa-per,we has been studied D（β）-vertex-distinguishing proper edge-coloring by probabilistic and giving colorings of a graph.The paper consists of five part.In the first part,we introduce some fundamental concepts that often used in the paper.In the second part,we discuss the properties of D（β）-vertex-distinguishing proper edge-coloring and,we has been obtained X’_3-vd（P_n） and X’_3-vd（C_n）,by induction we has gotten the D（β）-vertex-distinguishing proper edge-coloring chromatic number of P_n,S_n,C_n,K_n,F_n,W_nIn the third part,we have discussed and obtained the D（β）-vertex-distinguishing proper edge-coloring chromatic number of S_m∨P_n∨P_n,F_m∨P_n with giving coloring of a graph.In the fourth part,we have discussed and obtained the D（β）-vertex-distinguishing proper edge-coloring chromatic number of C_m·P_n,C_m·S_n,C_m·C_n,C_m·F_n,C_m·W_n with giving coloring of a graph,whenβ=1,2,3.In the last part,With applying the general form of the Lovász lo-cal lemma,we have discussed and obtained that X’_2-vd（G）≤32d²,d≥4,X’_3-vd（G）≤8d^5/2,d≥6 and whenβ≥4,d≥4,X’_β-vd（G）≤2（?）for any simple graph G with maximum degree d.we has gotten another upper bounds for D（2）-vertex-distinguishing proper edge-coloring chromatic number X’_2-vd（G）≤△+1+（?）for the simple graph with maximum degree△≥16² ln 6,minimum degreeδ≥16（?） With applying the general form of the Lovász local lemma by another method更多还原