图的corona积的局部反魔幻着色数  

The local antimagic chromatic number of the corona product of graphs

作　　者：杨雪 边红[1] 于海征[2] 丁吉丽 YANG Xue;BIAN Hong;YU Haizheng;DING Jili(School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China;College of Mathematics and System Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017 [2]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《厦门大学学报（自然科学版）》2022年第2期167-173,共7页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11761070,61662079);2020年新疆维吾尔自治区自然基金新疆大学联合项目(2021D01C078);2020年新疆师范大学一流专业、一流课程项目。

摘　　要：令G=(V(G),E(G))是具有n个顶点、m条边的连通简单图.称一个双射f:E(G)→{1,2,…,|E(G)|}为图G的一个局部反魔幻标号,如果f满足对于G中任意两个相邻的顶点u和v都有w(u)≠w(v),其中w(u)=∑e∈E(u)f(e),E(u)是与点u相关联的边的集合.若对图G的顶点v着颜色w(v),则图G的任何一个局部反魔幻标号自然地导出图G的一个正常点着色.一个图G的局部反魔幻着色数是其局部反魔幻标号中所用的最少颜色数,记为χla(G).给定两个简单图G和H,图G和H的corona积,记为GH,它是通过取图G的一个拷贝和|V(G)|个图H的拷贝,然后把图G的第i个顶点与第i个图H的拷贝中的每个顶点相连而得到的图.本文给出了友谊图Fn、星图Sn与空图Km(m≥1)的corona积的局部反魔幻着色数的确切值.Let G=(V(G);E(G))be a connected simple graph with n vertices and m edges.A bijection f:E→{1,2,…,m}is called local antimagic labeling,if for any two adjacent vertices u and v of G,we have w(u)≠w(v),where w(u)=∑e∈E(u)f(e),and E(u)is the set of edges incident to u.Any local antimagic labeling of graph G induces a proper vertex coloring of G,where the vertex v is assigned the color w(v).The local antimagic chromatic number of graph G,denotedχla(G),is the minimum number of colors taken over all colorings induced by local antimagic labeling of G.Given two simple graphs G and H,the corona product of G and H,denoted by GH,which is obtained by taking one copy of G and|V(G)|copies of H,and join the i-th vertex in G to every vertex of i-th copy of H.In this paper,we present the exactly values of local antimagic chromatic numbersχla(GKm)for the corona product of a graph G with the empty graph Km for m≥1,where G is a friendship graph Fn or a star Sn.

关 键 词：局部反魔幻标号 局部反魔幻着色数 corona积 

分 类 号：O157.5[理学—数学]