P_(m)^(2)×Pn的r-多彩着色  

On r-Hued Coloring of P_(m)^(2)×Pn

作　　者：张春梅[1] 史雅馨 李越锋 ZHANG Chunmei;SHI Yaxin;LI Yuefeng(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第6期663-670,共8页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金“图和有向图的任意可分性的研究”(11961067)。

摘　　要：图G的(k,r)-着色是图G的一个正常k-着色,并满足G中的每一个顶点的邻点的颜色数至少为这个顶点的度d(v)和r的最小值.使得图G有(k,r)-着色的最小整数k称为图G的r-多彩色数,用χr(G)表示.研究了路的平方图和路的直积图的r-多彩着色,得到了r-多彩着色数.A(k,r)-coloring of G is a proper coloring with k colors such that for every vertex v with degree d(v)in G,the color number of the neighbors of v is at least min{d(v),r}.The smallest integer k such that G has an(k,r)-coloring is called the r-hued chromatic number and denoted byχr(G).In this paper,we study the r-hued coloring of direct product of path with the square of path,and obtain its r-hued chromatic number.

关 键 词：(k r)-着色 r-多彩着色数 直积图 路的平方图 

分 类 号：O157.5[理学—数学]