图mn(Pt)的邻点可区别的I-均匀全染色  

Incidence-Adjacent Vertex Distinguishing Equitable Total Coloring of m_(n)(P_(t))

作　　者：张婷 张修雪 杜佳 ZHANG Ting;ZHANG Xiu-xue;DU Jia(Normal School,Lanzhou University of Arts and Science,Lanzhou 730010,China;School of Digital Medial,Lanzhou University of Arts and Science,Lanzhou 730010,China)

机构地区：[1]兰州文理学院教育学院,甘肃兰州730000 [2]兰州文理学院数字媒体学院,甘肃兰州730000

出　　处：《数学的实践与认识》2024年第2期167-174,共8页Mathematics in Practice and Theory

基　　金：2023年甘肃省高等学校人才培养质量提升项目“应用型本科院校大学生科学思维的培养与研究”;甘肃省高等学校创新能力提升项目(2019B-195);兰州文理学院校级科研项目(2020QNRC09)。

摘　　要：针对广义Mycielski图的结构特征,提出了基于色调整技术的局部均匀染色法,这种染色法能够将较大图的染色转化为较小图的染色,简化染色过程,提高染色效率.利用基于色调整技术的局部均匀染色法和函数构造法研究给出了第二类广义Mycielski图mn(Pt)的邻点可区别的I-均匀全染色,得到了其邻点可区别的I-均匀全色数,结果验证了这类图满足邻点可区别I-均匀全染色猜想.According to the structural characteristics of generalized Mycielski graphs,a local equitable coloring method based on color adjustment technology is proposed.This method can transform the coloring of larger graphs into that of smaller graphs,simplify the coloring process and improve the coloring eficiency.In this paper,by using the local equitable coloring method based on the color adjustment technique and the function construction methods,we study and give the adjacent vertex distinguishing equitable total coloring of the second kind of general Mycielski graphs m_(n)(P_(t)),obtained the chromatic numbers of them.The results verify that this kind of graphs satisfy the AVDETC conjecture.

关 键 词：第二类广义Mycielski图 基于色调整技术的局部均匀染色法 邻点可区别I-均匀全染色 

分 类 号：O157.5[理学—数学]