2019
DOI: 10.1016/j.amc.2018.09.056
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Linear bounds on nowhere-zero group irregularity strength and nowhere-zero group sum chromatic number of graphs

Abstract: We investigate the group irregularity strength, s g (G), of a graph, i.e. the least integer k such that taking any Abelian group G of order k, there exists a function f : E(G) → G so that the sums of edge labels incident with every vertex are distinct. So far the best upper bound on s g (G) for a general graph G was exponential in n − c, where n is the order of G and c denotes the number of its components. In this note we prove that s g (G) is linear in n, namely not greater than 2n. In fact, we prove a strong… Show more

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Cited by 4 publications
(4 citation statements)
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“…The corresponding problem in the case of simple graphs was considered in [2,3]. For Γ = (Z 2 ) m the problem was raised in [11].…”
Section: Letmentioning
confidence: 99%
“…The corresponding problem in the case of simple graphs was considered in [2,3]. For Γ = (Z 2 ) m the problem was raised in [11].…”
Section: Letmentioning
confidence: 99%
“…The corresponding problem in the case of simple graphs was considered in [2,3,4]. For Γ = (Z 2 ) m the problem was raised in [13].…”
Section: Letmentioning
confidence: 99%
“…For a non-connected graph G with no K 2 components, it is known that k(G) ≤ 2|V(G)| [10]. Moreover Anholcer and Cichacz proved the following.…”
Section: Introductionmentioning
confidence: 96%