Group Irregular Labelings of Disconnected Graphs

Authors

  • Marcin Anholcer
  • Sylwia Cichacz-Przenioslo AGH University of Science and Technology

DOI:

https://doi.org/10.11575/cdm.v12i2.62601

Keywords:

Irregularity strength, Graph weighting, Graph labeling, Abelian group

Abstract

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.

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Published

2017-11-27

Issue

Vol. 12 No. 2 (2017)

Section

Articles

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