Distance magic circulant graphs

Sylwia Cichacz; Dalibor Froncek

doi:10.1016/j.disc.2015.07.002

Distance magic circulant graphs

Sylwia Cichacz, Dalibor Froncek

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Let G=(V,E) be a graph of order n. A distance magic labeling of G is a bijection ℓ:V → {1,2,...,n} for which there exists a positive integer k such that Σ_x∈N(v) ℓ(x)=k for all v ∈ V, where N(v) is the neighborhood of v. In this paper we deal with circulant graphs C_n(1,p). The circulant graph C_n(1,p) is the graph on the vertex set V={x₀,x₁,...,x_n-1} with edges (x_i,x_i+p) for i=0,...,n-1 where i+p is taken modulo n. We completely characterize distance magic graphs C_n(1,p) for p odd. We also give some sufficient conditions for p even. Moreover, we also consider a group distance magic labeling of C_n(1,p).

Original language	English (US)
Pages (from-to)	84-94
Number of pages	11
Journal	Discrete Mathematics
Volume	339
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2015.07.002
State	Published - Jan 6 2016

Bibliographical note

Funding Information:
The author was supported by the National Science Centre Grant No. 2011/01/D/ST1/04104 .

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

Circulant graphs
Distance magic labeling
Group distance magic labeling

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abstract = "Let G=(V,E) be a graph of order n. A distance magic labeling of G is a bijection ℓ:V → {1,2,...,n} for which there exists a positive integer k such that Σx∈N(v) ℓ(x)=k for all v ∈ V, where N(v) is the neighborhood of v. In this paper we deal with circulant graphs Cn(1,p). The circulant graph Cn(1,p) is the graph on the vertex set V={x0,x1,...,xn-1} with edges (xi,xi+p) for i=0,...,n-1 where i+p is taken modulo n. We completely characterize distance magic graphs Cn(1,p) for p odd. We also give some sufficient conditions for p even. Moreover, we also consider a group distance magic labeling of Cn(1,p).",

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author = "Sylwia Cichacz and Dalibor Froncek",

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Distance magic circulant graphs

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Keywords

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