Group irregularity strength of connected graphs

Marcin Anholcer (), Sylwia Cichacz () and Martin Milanic̆ ()
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Marcin Anholcer: Poznań University of Economics
Sylwia Cichacz: University of Primorska, UP FAMNIT
Martin Milanic̆: University of Primorska, UP FAMNIT

Journal of Combinatorial Optimization, 2015, vol. 30, issue 1, No 1, 17 pages

Abstract: Abstract We investigate the group irregularity strength ( $$s_g(G)$$ s g ( G ) ) of graphs, that is, we find the minimum value of $$s$$ s such that for any Abelian group $$\mathcal G $$ G of order $$s$$ s , there exists a function $$f:E(G)\rightarrow \mathcal G $$ f : E ( G ) → G such that the sums of edge labels at every vertex are distinct. We prove that for any connected graph $$G$$ G of order at least $$3$$ 3 , $$s_g(G)=n$$ s g ( G ) = n if $$n\ne 4k+2$$ n ≠ 4 k + 2 and $$s_g(G)\le n+1$$ s g ( G ) ≤ n + 1 otherwise, except the case of an infinite family of stars. We also prove that the presented labelling algorithm is linear with respect to the order of the graph.

Keywords: Irregularity strength; Graph labelling; Abelian group; 05C15; 05C78 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-013-9628-6

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