Group irregularity strength of connected graphs

Marcin Anholcer , Sylwia Cichacz , Martin Milanic̆

Abstract

We investigate the group irregularity strength (sg(G)) of graphs, that is, we find the minimum value of s such that for 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. We prove that for any connected graph G of order at least 3, sg(G)=n if n≠4k+2 and sg(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.
Author Marcin Anholcer (WIiGE / KBO)
Marcin Anholcer,,
- Department of Operations Research
, Sylwia Cichacz - AGH University of Science and Technology (AGH), MNiSW [80]
Sylwia Cichacz,,
-
, Martin Milanic̆ - University of Primorska
Martin Milanic̆,,
-
Journal seriesJournal of Combinatorial Optimization, ISSN 1382-6905, (A 25 pkt)
Issue year2015
Vol30
No1
Pages1-17
Publication size in sheets0.8
Keywords in EnglishIrregularity strength; Graph labelling; Abelian group
ASJC Classification1703 Computational Theory and Mathematics; 1706 Computer Science Applications; 2604 Applied Mathematics; 2606 Control and Optimization; 2607 Discrete Mathematics and Combinatorics
DOIDOI:10.1007/s10878-013-9628-6
URL https://link.springer.com/article/10.1007/s10878-013-9628-6
Languageen angielski
Score (nominal)25
Score sourcejournalList
ScoreMinisterial score = 25.0, 10-01-2020, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 10-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 6; Scopus SNIP (Source Normalised Impact per Paper): 2015 = 1.225; WoS Impact Factor: 2015 = 1.08 (2) - 2015=1.101 (5)
Citation count*10 (2020-09-23)
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