Wn□Pm的r-hued染色
On r-hued coloring of Wn□Pm
史雅馨 1刘凤霞 1蔡华2
作者信息
- 1. 新疆大学数学与系统科学学院,新疆乌鲁木齐 830046
- 2. 昌吉学院数学与数据科学学院,新疆昌吉 831199
- 折叠
摘要
图G的(k,r)-染色是对图G用k种颜色进行正常染色,使得图G任一点v的邻点至少染min{r,d(v)}种不同的颜色.使图G有一个(k,r)-染色的最小的整数k称为图G的r-hued色数,用xr(G)来表示.图G和H的笛卡尔乘积图记为G□H,其顶点集为V(G)×V(H),(u1,v1)与(u2,v2)相邻当且仅当u1=u2,v1v2∈E(H)或v1=v2,u1u2∈E(G).确定了Wn□Pm的r-hued色数.
Abstract
A(k,r)-coloring of a graph G is a proper k-coloring of graph G such that the neighbors of any vertex receive at least min｛r,d(v)}different colors.The smallest positive integral k such that graph G has a(k,r)-coloring is defined as the r-hued chromatic number and denoted by xr(G).The Cartesian product of two graphs G and H,denoted by G□H,has vertex set V(G)× V(H),where(u1,v1)and(u2,v2)are adjacent if and only if either u1=u2 and v1v2 ∈ E(G),or v1=v2 and u1u2 ∈ E(G).In this paper,the r-hued chromatic number of Wn□Pm is determined.
关键词
(k,r)-染色/r-hued色数/笛卡尔乘积图Key words
(k,r)-coloring/r-hued chromatic number/Cartesian product of graphs引用本文复制引用
基金项目
新疆维吾尔自治区自然科学基金资助项目(2022D01C02)
国家自然科学基金地区项目(11961067)
出版年
2024
NETL
NSTL
万方数据