摘要
如果可以给图G的边用集合{±1,±2,…,±k}中的元素标号,使得对G每个顶点v,其标号,即所有与其相邻的边的标号之和,都落在集合{±1,±2,…,±k}中,且|e(i)-e(-i)|≤1和|v(i)-v(-i)|≤1,其中v(i)和e(i)(1≤i≤k)分别是标号为i的顶点数和边数,那么就称该图G为Hk-cordial的.本文证明了除了K2以外,每棵树都是H3-cordial的.
A graph G is called to be Hk-cordial, if it is possible to label the edges with the numbers from the set {±1,±2,.. ,±k} in such a way that, at each vertex v, the label of it, that is the algebraic sum of the labels on the edges incident with v, is in the set {±1,±2,.. ,±k} and the inequalities ｜e（i）-e（-i）｜≤1 and ｜v（i）-v（-i）≤1 are also satisfied for each i with 1≤0≤k,where v（i） and e（i） are, respectively, the numbers of vertices and edges labeled with i. In the paper, every tree is shown to be H3-cordial, except the complete graph K2.
出处
《数学研究》
CSCD
2013年第1期64-71,共8页
Journal of Mathematical Study
基金
supported by NSFC(11171279,11226288)
