森林的全顶点不规则强度
组合数学
2011-03-11 v1
摘要
我们研究一个称为全顶点不规则强度()的图参数，即最小的，使得存在一个边和顶点的标号，赋予的每一对顶点不同的加权度。我们证明，对于每个没有2度顶点且没有孤立顶点的森林，有，其中是中悬挂顶点的数量。Nurdin等人最近证明了关于树的更强结果。
引用
@article{arxiv.1103.2087,
title = {Total Vertex Irregularity Strength of Forests},
author = {Marcin Anholcer and Michał Karoński and Florian Pfender},
journal= {arXiv preprint arXiv:1103.2087},
year = {2011}
}
备注
The stronger results for trees were recently proved by Nurdin et al. (Nurdin, Baskoro E.T., Salman A.N.M., Gaos N.N., On the Total Vertex Irregularity Strength of Trees, Discrete Mathematics 310 (2010), 3043-3048.). However we decided to publish our paper for two reasons. Firstly, we consider more general case of forests, not only trees. Secondly, we use different proof technique