图mP_2∪mC_t(3≤t≤10)的点可区别正常边染色  

On the Vertex-distinguishing Proper Edge-Coloring of mP_2∪mC_t(3≤t≤10)

作　　者：高毓平[1] 王治文[2] 陈祥恩[1] 姚兵[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：《山西大学学报（自然科学版）》2012年第3期440-447,共8页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(61163037;61163054);宁夏大学科学研究基金((E)ndzr10-7);宁夏自然科学基金(NZ1154);西北师范大学科技创新工程项目(nwnu-kjcxgc-03-61)

摘　　要：图G的正常边染色称为是点可区别的,如果对G的任意两个不同的顶点u,v,与u关联的边的颜色构成的集合异于与v关联的边的颜色构成的集合.对图G进行点可区别正常边染色所需要的最少颜色数称为是G的点可区别正常边色数,记为χ′s(G).通过将路和圈填装到完全图,我们给出了mP2∪mCt的点可区别正常边色数的一个刻画,并利用递归染色的方式,得到了χ′s(mP2∪mCt)(3≤t≤10).A k-proper edge coloring of a simple graph G is called vertex-distinguishing if for arbitrary two different vertices u and v,the set of colors assigned to the edges incident to u differs from the set of colors assigned to the edges incident to v.The minimum number of colors required for a vertex-distinguishing proper edge-coloring of a simple graph G is called vertex-distinguishing proper edge chromatic number of G and is denoted by χ′s(G).In this paper,a description of vertex-distinguishing proper edge chromatic number of mP2∪mCt is given by packing paths and cycles to complete graphs,and χ′s(mP2∪mCt)(3≤t≤10) are received by recursively coloring to graphs.

关 键 词：图 点可区别正常边染色 点可区别正常边色数 

分 类 号：O15[理学—数学]