图mC_(8)的点可区别Ⅰ-全染色和Ⅵ-全染色  

Vertex-DistinguishingⅠ-Total Colorings andVertex-DistinguishingⅥ-Total Colorings of Graph mC_(8)

作　　者：杨晗 陈祥恩 YANG Han;CHEN Xiang’en(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2021年第2期241-249,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11761064,61163037).

摘　　要：通过构造以色集合和空集为元素的矩阵,利用色集合事先分配法及具体的染色方案,给出图mC_(8)的最优点可区别Ⅰ-全染色和最优点可区别Ⅵ-全染色,进而确定图mC_(8)的点可区别Ⅰ-全色数和点可区别Ⅵ-全色数.结果表明,VDITC猜想和VDVITC猜想对图mC_(8)成立.By constructing a matrix which was composed of color sets and empty set as the elements,using t he distributing method of color sets in advance and specific coloring scheme,we gave the best vertex-distinguishing Ⅰ-total colorings(VDITC)and the best vertex-distingui shing Ⅵ-total colorings(VDVITC)of graph mC_(8).Thus vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph mC_(8)were determined.The results show that the VDITC conjecture and VDVITC conjecture are valid for graph mC_(8).

关 键 词：圈 不交并 点可区别Ⅰ-全染色 点可区别Ⅵ-全染色 点可区别Ⅰ-全色数 点可区别Ⅵ-全色数 

分 类 号：O157.5[理学—数学]