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中文摘要：
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u，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Ie（i）-e（-i）I≤1和lu（i）-u（-i）1≤1，其中t心）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．本文证明了除了尥以外，每棵树都是H3-cordial的．
英文摘要：
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.
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