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Note on group irregularity strength of disconnected graphs

Note on group irregularity strength of disconnected graphs AbstractWe investigate the group irregularity strength (sg(G)) of graphs, i.e. the smallest value of s such that taking any Abelian group 𝓖 of order s, there exists a function f : E(G) → 𝓖 such that the sums of edge labels at every vertex are distinct. So far it was not known if sg(G) is finite for disconnected graphs. In the paper we present some upper bound for all graphs. Moreover we give the exact values and bounds on sg(G) for disconnected graphs without a star as a component. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

Note on group irregularity strength of disconnected graphs

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Publisher
de Gruyter
Copyright
© 2018 Anholcer et al., published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0017
Publisher site
See Article on Publisher Site

Abstract

AbstractWe investigate the group irregularity strength (sg(G)) of graphs, i.e. the smallest value of s such that taking any Abelian group 𝓖 of order s, there exists a function f : E(G) → 𝓖 such that the sums of edge labels at every vertex are distinct. So far it was not known if sg(G) is finite for disconnected graphs. In the paper we present some upper bound for all graphs. Moreover we give the exact values and bounds on sg(G) for disconnected graphs without a star as a component.

Journal

Open Mathematicsde Gruyter

Published: Mar 2, 2018

Keywords: Irregularity strength; Graph weighting; Graph labeling; Abelian group; 05C15; 05C78

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