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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) Indonesian Journal of Combinatorics
Anak Agung Gede Ngurah
Department Of Civil Engineering, Universitas Merdeka Malang Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management Electrical & Electronics Engineering

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On distance labelings of 2-regular graphs Anak Agung Gede Ngurah; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.1.3

Abstract

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.
On the super edge-magic deficiency of join product and chain graphs Anak Agung Gede Ngurah; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2019.7.1.12

Abstract

A graph G of order ∣V(G)∣ = p and size ∣E(G)∣ = q is called super edge-magic if there exists a bijection f : V(G) ∪ E(G) → {1, 2, 3, ⋯, p + q} such that f(x) + f(xy) + f(y) is a constant for every edge xy ∈ E(G) and f(V(G)) = {1, 2, 3, ⋯, p}. Furthermore, the super edge-magic deficiency of a graph G, μs(G), is either the minimum nonnegative integer n such that G ∪ nK1 is super edge-magic or  + ∞ if there exists no such integer n. In this paper, we study the super edge-magic deficiency of join product of a graph which has certain properties with an isolated vertex and the super edge-magic deficiency of chain graphs.
New families of star-supermagic graphs Anak Agung Gede Ngurah
Indonesian Journal of Combinatorics Vol 4, No 2 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2020.4.2.4

Abstract

A simple graph G admits a K1,n-covering if every edge in E(G) belongs to a subgraph of G isomorphic to K1,n. The graph G is K1,n-supermagic if there exists  a bijection f : V(G) ∪ E(G) → {1, 2, 3,..., |V(G) ∪ E(G)|} such that for every subgraph H' of G isomorphic to K1,n,  ∑v ∈ V(H')  f(v) + ∑e ∈ E(H') f(e) is  a constant and f(V(G)) = {1, 2, 3,..., |V(G)|}. In such a case, f is called a K1,n-supermagic labeling of G.  In this paper, we give a method how to construct K1,n-supermagic graphs from the old ones.
On (super) edge-magic deficiency of some classes of graphs Ngurah, Anak Agung Gede; Simanjuntak, Rinovia; Baskoro, Edy Tri
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2025.13.1.4

Abstract

A graph G of order p and size q is called edge-magic total if there exists a bijection ϕ from V(G)∪E(G) to the set {1, 2, …, p + q} such that ϕ(s)+ϕ(st)+ϕ(t) is a constant for every edge st in E(G). An edge-magic total graph with ϕ(V(G)) = {1, 2, …, p} is called super edge-magic total. Furthermore, the edge-magic deficiency of a graph G is the smallest integer n ≥ 0 such that G ∪ nK1 is edge-magic total. The super edge-magic deficiency of a graph G is either the smallest integer n ≥ 0 such that G ∪ nK1 is super edge-magic total or +∞ if there exists no such integer n. In this paper, we study the (super) edge-magic deficiency of join product graphs and 2-regular graphs.
Co-Authors Baskoro, Edy Tri Rinovia Simanjuntak Rinovia Simanjuntak Simanjuntak, Rinovia