NDLI: Note on Distance Magic Products $$G\circ C

Content Provider	Springer Nature Link
Author	Cichacz, Sylwia Anholcer, Marcin
Copyright Year	2014
Abstract	A distance magic labeling of a graph $$G=(V,E)$$ of order $$n$$ is a bijection $$l :V \rightarrow \{1, 2,\ldots , n\}$$ with the property that there is a positive integer $$k$$ (called magic constant) such that $$w(x) = k$$ for every $$x \in V$$ . 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 $$G\circ C_4$$ was posted in Arumugam et al. (J Indonesian Math Soc 11–26, 2011). We give necessary and sufficient conditions for the graphs $$K_{m,n}\circ C_4$$ to be distance magic. We also show that the product $$C^{(t)}_3\circ C_4$$ of the Dutch Windmill Graph and the cycle $$C_4$$ is not distance magic for any $$t>1$$ .
Ending Page	1124
Page Count	8
Starting Page	1117
File Format	PDF
ISSN	09110119
e-ISSN	14355914
Journal	Graphs and Combinatorics
Issue Number	5
Volume Number	31
Language	English
Publisher	Springer Japan
Publisher Date	2014-05-22
Publisher Place	Tokyo
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Sigma labeling Composition of graphs Graph labeling Magic constant Graph labelling (graceful graphs, bandwidth, etc.) Engineering Design Lexicographic product of graphs Combinatorics Distance magic labeling
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science

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