Group irregularity strength of connected graphs
Marcin Anholcer , Sylwia Cichacz , Martin Milanic̆
AbstractWe 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.
|Journal series||Journal of Combinatorial Optimization, ISSN 1382-6905, (A 25 pkt)|
|Publication size in sheets||0.8|
|Keywords in English||Irregularity strength; Graph labelling; Abelian group|
|ASJC Classification||; ; ; ;|
|Score|| = 25.0, 10-01-2020, ArticleFromJournal|
= 25.0, 10-01-2020, ArticleFromJournal
|Publication indicators||= 6; : 2015 = 1.225; : 2015 = 1.08 (2) - 2015=1.101 (5)|
|Citation count*||10 (2020-09-23)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.