Note on Distance Magic Products G∘C4

Marcin Anholcer , Sylwia Cichacz

Abstract

A distance magic labeling of a graph G=(V,E) of order n is a bijection l:V→{1,2,…,n} with the property that there is a positive integer k (called magic constant) such that w(x)=k for every x∈V. If a graph G admits a distance magic labeling, then we say that G is a distance magic graph. In the case of non-regular graph G, the problem of determining whether there is a distance magic labeling of the lexicographic product G∘C4 was posted in Arumugam et al. (J Indonesian Math Soc 11–26, 2011). We give necessary and sufficient conditions for the graphs Km,n∘C4 to be distance magic. We also show that the product C(t)3∘C4 of the Dutch Windmill Graph and the cycle C4 is not distance magic for any t>1.
Author Marcin Anholcer (WIiGE / KBO)
Marcin Anholcer,,
- Department of Operations Research
, Sylwia Cichacz - AGH University of Science and Technology (AGH)
Sylwia Cichacz,,
-
Journal seriesGraphs and Combinatorics, ISSN 0911-0119, (A 20 pkt)
Issue year2015
Vol31
No5
Pages1117-1124
Publication size in sheets0.5
Keywords in EnglishDistance magic labeling, Magic constant, Sigma labeling, Graph labeling, Composition of graphs, Lexicographic product of graphs
ASJC Classification2607 Discrete Mathematics and Combinatorics; 2614 Theoretical Computer Science
Languageen angielski
Score (nominal)20
Score sourcejournalList
ScoreMinisterial score = 15.0, 10-01-2020, ArticleFromJournal
Ministerial score (2013-2016) = 20.0, 10-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 3; Scopus SNIP (Source Normalised Impact per Paper): 2015 = 1.217; WoS Impact Factor: 2015 = 0.48 (2) - 2015=0.478 (5)
Citation count*7 (2020-10-18)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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