W_(n)⊙P_(m)和C_(n)⊙S_(m)的r-hued染色  

On r-hued Coloring of W_(n)⊙P_(m) and C_(n)⊙S_(m)

作　　者：唐梦 刘凤霞[1] TANG Meng;LIU Fengxia(College of Mathematics and System Science,Xinjiang University,Urumqi 830046,Xinjiang)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《四川师范大学学报（自然科学版）》2023年第5期646-651,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11961067)。

摘　　要：图G和H的Corona乘积图记为G⊙H,它是复制一个图G以及复制|V(G)|个图H,把图G的第i个顶点跟复制的第i个图H的每个顶点相连.图G的(k,r)-染色是用k种颜色对图G进行正常染色,使得点v的所有邻点至少染min{r,d(v)}种不同的颜色,其中d(v)是图G中顶点v的度数.把图G的具有(k,r)-染色的最小正整数k称为r-hued色数,用χ_(r)(G)表示,通过对r-hued染色的定义,得到W_(n)⊙P_(m)和C_(n)⊙S_(m)的r-hued色数.The Corona product graph of two graphs G and H is denoted by G⊙H,which is obtained by taking one copy of G and|V(G)|copies of H where ith vertex of G is adjacent to every vertex in the ith copy of H.A(k,r)-coloring of a graph G is a proper k-coloring of graph G such that the neighbors of any vertex v receive at least min{r,d(v)}different colors,where d(v)is the degree of vertex v of graph G.The smallest integer k such that G has a(k,r)-coloring is called the r-hued chromatic number and denoted by χ_(r)(G).By the definitions of r-hued coloring,the r-hued chromatic number of W_(n)⊙P_(m) and C_(n)⊙S_(m) are obtained.

关 键 词：(k r)-染色 r-hued色数 Corona乘积图 

分 类 号：O157.5[理学—数学]