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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Simanjuntak, Rinovia
Institut Teknologi Bandung
Electrical & Electronics Engineering

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Further results on the total vertex irregularity strength of trees Susanto, Faisal; 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.2025.13.1.9

Abstract

We investigate the total vertex irregularity strength of trees with specific characteristics. Initially, we categorize trees into three distinct groups: types A, B, and C. Subsequently, we calculate tvs(T) for all type A trees T where the maximum degree is at least three. Additionally, we provide the value of tvs(T) whenever T is a tree of types B or C with maximum degree at least three and large number of exterior vertices. Finally, we propose a conjecture related to tvs(T) where T is a non-path tree of types B or C with few exterior vertices. 
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.
D-antimagic labelings arising from completely separating systems Wulandari, Risma Yulina; Simanjuntak, Rinovia; Saputro, Suhadi Wido
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (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.2025.13.2.2

Abstract

Let D be a non-empty subset of the distance set {0,1,…, diam(G)}. A graph G is D-antimagic if there exists a bijection f:V(G)→{1,2,…,|V(G)|} such that for every pair of distinct vertices x and y, wD(x) ≠ wD(y), where wD(x) = Σz∈ND(x)f(z) is the D-weight of x and ND(x) = {z|d(x,z)∈D} is the D-neighbourhood of x. It was conjectured that a graph G is D-antimagic if and only if each vertex in G has a distinct D-neighborhood. A completely separating system (CSS) in the finite set {1,2,…,n} is a collection ? of subsets of {1,2,…,n} in which for each pair a≠b∈{1,2,…,n}, there exist A,B∈? such that a∈A−B and b∈B−A.In this paper, we provide evidence to support the conjecture mentioned earlier by using Roberts' completely separating systems to define D-antimagic labelings for certain graphs. In particular, we show that if G and H are D-antimagic graphs with labelings constructed from Roberts' CSS, then the vertex-deleted subgraph, G−{v} and the vertex amalgamation of G and H are also D-antimagic. Additionally, we partially answer an open problem of Simanjuntak et al. (2021) by constructing {1}-antimagic labelings for some disjoint unions of paths.
On the relations among edge magic total, edge antimagic total, and ASD-antimagic graphs Pancahayani, Sigit; Simanjuntak, Rinovia; Baca, Martin; Semanicova-Fenovcıkova, Andrea; Uttunggadewa, Saladin
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (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.2025.13.2.11

Abstract

Let G be a simple and finite graph of order p and size q. The graph G is said to be edge magic total (EMT) if there is a bijection λ:V(G)∪E(G)→{1,2,…,p+q} such that all edge sums λ(x)+λ(xy)+λ(y), xy∈E(G), are the same. If all edge sums are pairwise distinct, then G is called edge antimagic total (EAT). Let t be a positive integer that satisfies C(t+1,2)≤q<C(t+2,2). The graph G is said to have an ascending subgraph decomposition (ASD) if G can be decomposed into t subgraphs H1,H2,…,Ht without isolated vertices such that Hi is isomorphic to a proper subgraph of Hi+1 for 1≤i≤t−1. A graph that admits an ascending subgraph decomposition is called an ASD graph. An ASD graph G is said to be ASD-antimagic if there exists a bijection f:V(G)∪E(G)→{1,2,…,p+q} such that all subgraph weights w(Hi)=∑v∈V(Hi)f(v)+∑e∈E(Hi)f(e), 1≤i≤t, are distinct. In this paper, we provide constructions of ASD-antimagic graphs arising from EMT or EAT graphs.
Co-Authors Anak Agung Gede Ngurah Baca, Martin Baskoro, Edy Tri Pancahayani, Sigit Saputro, Suhadi Wido Semanicova-Fenovcıkova, Andrea Susanto, Faisal Uttunggadewa, Saladin Wulandari, Risma Yulina