Harmonic trees

被引：24

作者：

Grünewald, S ^{[1
]}

机构：

[1] Univ Bielefeld, Forschungsschwerpunkt Mathematisierung, D-33501 Bielefeld, Germany

来源：

APPLIED MATHEMATICS LETTERS | 2002年 / 15卷 / 08期

关键词：

harmonic graphs; walks in graphs; finite and infinite trees;

D O I：

10.1016/S0893-9659(02)00076-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A graph G is defined to be harmonic if there is a constant lambda (necessarily a natural number) such that, for every vertex upsilon, the sum of the degrees of the neighbors of upsilon equals lambdad(G)(upsilon) where d(G)(upsilon) is the degree of upsilon. We show that there is exactly one finite harmonic tree for every lambda epsilon N, and we give a recursive construction for all infinite harmonic trees. (C) 2002 Elsevier Science Ltd. All rights reserved.

引用

页码：1001 / 1004

页数：4