F_(m)、P_(n)⊙F_(m)和C_(n)⊙F_(m)的r-hued染色研究  

On r-hued Coloring of F_(m),P_(n)⊙F_(m)and C_(n)⊙F_(m)

作　　者：西日尼阿依·努尔麦麦提 刘凤霞[2] SHIRINAY Nurmamat;LIU Fengxia(College of Mathematics and Statistics,Kashgar University,Kashgar 844000,Xinjiang;College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,Xinjiang)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844000 [2]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）》2024年第2期269-274,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11961067)。

摘　　要：给定2个图G和H,它们的corona乘积图记为G⊙H,是将图G拷贝一份、图H拷贝|V(G)|份,图G的第i个顶点和图H的第i个拷贝份的每个顶点连边而得到的图.图G的(k,r)-染色是图G正常k-染色,使得度数为d的每个顶点的邻点至少染min{d,r}种不同的颜色.r-hued染色数是最小正整数k,使得图G具有(k,r)-染色,用χr(G)来表示.主要讨论F_(m),P_(n)⊙F_(m)和C_(n)⊙F_(m)的r-hued染色数.Given two graphs G and H,the corona product of G and H,denoted by G⊙H,is a graph obtained by taking one copy of G and|V(G)|copies of H,where the 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 G such that the neighbors of each vertex of degree d will receive at least min{d,r}different colors.The r-hued chromatic number,is the minimum integer k such that graph G has a(k,r)-coloring,denoted byχr(G).In this paper,we mainly discuss the r-hued chromatic number of F_(m),P_(n)⊙F_(m)and C_(n)⊙F_(m).

关 键 词：(k r)-染色 r-hued色数 corona乘积图 

分 类 号：O157.5[理学—数学]