On distance labelings of 2-regular graphs
| Main Authors: | Ngurah, Anak Agung Gede; Department of Civil Engineering, Universitas Merdeka Malang Indonesia, Simanjuntak, Rinovia; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2021
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/879 https://www.ejgta.org/index.php/ejgta/article/view/879/pdf_158 |
Daftar Isi:
- 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.