Wn⊙Pm和Cn⊙Sm的r-hued染色

唐梦　刘凤霞

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.

关键词：（k，r）-染色; r-hued色数; Corona乘积图

中图分类号：O157.5 文献标志码：A 文章编号：1001-8395（2023）05-0646-06

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On r-hued Coloring of W_n⊙P_mand  C_n⊙S_mTANG Meng，LIU Fengxia（College of Mathematics and System Science， Xinjiang University， Urumqi 830046， Xinjiang）

Abstract：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 χr（G）. By the definitions of r-hued coloring， the r-hued chromatic number of W_n⊙P_mand C_n⊙S_mare obtained.

Keywords：（k，r）-coloring; r-hued chromatic number; Corona product of graphs

2020 MSC：05C15（編辑余毅）