Group Irregular Labelings of Disconnected Graphs

Contributions to Discrete Mathematics

Marcin Anholcer ; Sylwia Cichacz-Przenioslo

关键词: Irregularity strength, Graph weighting, Graph labeling, Abelian group;   

学科分类：社会科学、人文和艺术（综合）

来源: University of Calgary * Department of Mathematics and Statistics

【 摘 要 】

We investigate the \textit{group irregularity strength} ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\gr$ of order $s$, there exists a function $f:E(G)\rightarrow \gr$ such that the sums of edge labels at every vertex are distinct. We give the exact values and bounds on $s_g(G)$ for chosen families of disconnected graphs. In addition we present some results for the \textit{modular edge gracefulness} $k(G)$, i.e. the smallest value of $s$ such that there exists a function $f:E(G)\rightarrow \zet_s$ such that the sums of edge labels at every vertex are distinct.

【 授权许可】

Unknown