On distance labelings of 2-regular graphs

Anak Agung Gede Ngurah, Rinovia Simanjuntak


Let G  be a graph with |V(G)| vertices and ψ :  V(G) → {1, 2, 3, ... , |V(G)|} be a bijective function. The weight of a vertex v ∈ V(G) under ψ is wψ(v) = ∑u ∈ N(v)ψ(u).  The function ψ is called a distance magic labeling of G, if wψ(v) is a constant for every v ∈ V(G).  The function ψ is called  an (a,d)-distance antimagic labeling of G, if the set of vertex weights is  a, a+d, a+2d, ... , a+(|V(G)|-1)d. A graph that admits a distance magic (resp. an (a,d)-distance antimagic) labeling is called  distance magic (resp.  (a,d)-distance antimagic).  In this paper, we characterize distance magic 2-regular graphs and   (a,d)-distance antimagic some classes of 2-regular graphs.


distance magic labeling, $(a,d)$-distance antimagic labeling, 2-regular graph

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DOI: http://dx.doi.org/10.5614/ejgta.2021.9.1.3


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