Group distance magic labeling of direct product of graphs

Marcin Anholcer , Sylwia Cichacz , Iztok Peterin , Aleksandra Tepeh


Let G = (V, E) be a graph and Γ  an Abelian group, both of order n. A group distance magic labeling of G is a bijection ℓ: V → Γ  for which there exists μ ∈ Γ  such that ∑ x ∈ N(v)ℓ(x) = μ for all v ∈ V, where N(v) is the neighborhood of v. In this paper we consider group distance magic labelings of direct product of graphs. We show that if G is an r -regular graph of order n and m = 4 or m = 8 and r is even, then the direct product Cm × G is Γ -distance magic for every Abelian group of order mn. We also prove that Cm × Cn is Zmn-distance magic if and only if m ∈ {4, 8} or n ∈ {4, 8} or m, n ≡ 0 mod 4. It is also shown that if m, n not≡ 0 mod 4 then Cm × Cn is not Γ -distance magic for any Abelian group Γ  of order mn.
Author Marcin Anholcer (WIiGE / KBO)
Marcin Anholcer,,
- Department of Operations Research
, Sylwia Cichacz - AGH University of Science and Technology (AGH), MNiSW [80]
Sylwia Cichacz,,
, Iztok Peterin - University of Maribor, Slovenia
Iztok Peterin,,
, Aleksandra Tepeh - University of Maribor, Slovenia
Aleksandra Tepeh,,
Journal seriesArs Mathematica Contemporanea, ISSN 1855-3966, e-ISSN 1855-3974, (A 30 pkt)
Issue year2015
Publication size in sheets0.7
Keywords in Englishdistance magic labeling, group labeling, strong product of graphs
ASJC Classification2602 Algebra and Number Theory; 2607 Discrete Mathematics and Combinatorics; 2608 Geometry and Topology; 2614 Theoretical Computer Science
Languageen angielski
Score (nominal)30
Score sourcejournalList
ScoreMinisterial score = 30.0, 10-01-2020, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 10-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 3; Scopus SNIP (Source Normalised Impact per Paper): 2015 = 1.473; WoS Impact Factor: 2015 = 0.985 (2) - 2015=0.919 (5)
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