W_(n)□P_(m)的r-hued染色  

On r-hued coloring of W_(n)□P_(m)

作　　者：史雅馨 刘凤霞[1] 蔡华 SHI Yaxin;LIU Fengxia;CAI Hua(College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,Xinjiang,China;College of Mathematics and Data Sciences,Changji University,Changji 831199,Xinjiang,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830046 [2]昌吉学院数学与数据科学学院,新疆昌吉831199

出　　处：《山东大学学报（理学版）》2024年第2期59-64,共6页Journal of Shandong University(Natural Science)

基　　金：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)。

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χ_(r)(G)来表示。图G和H的笛卡尔乘积图记为GH,其顶点集为V(G)×V(H),(u_(1),v_(1))与(u_(2),v_(2))相邻当且仅当u_(1)=u_(2),v_(1)v_(2)∈E(H)或v_(1)=v_(2),u_(1)u_(2)∈E(G)。确定了W_(n)□P_(m)的r-hued色数。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 byχ_(r)(G).The Cartesian product of two graphs G and H,denoted by G□H,has vertex set V(G)×V(H),where(u_(1),v_(1))and(u_(2),v_(2))are adjacent if and only if either u_(1)=u_(2) and v_(1)v_(2)∈E(G),or v_(1)=v_(2) and u_(1)u_(2)∈E(G).In this paper,the r-hued chromatic number of W_(n)□P_(m) is determined.

关 键 词：(k r)-染色 r-hued色数 笛卡尔乘积图 

分 类 号：O157.5[理学—数学]