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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) Journal of Mathematical and Fundamental Sciences Indonesian Journal of Combinatorics Journal La Multiapp Jurnal Locus Penelitian dan Pengabdian
Simanjuntak, Rinovia
Combinatorial Mathematics Research Group, Faculty Of Mathematics And Natural Sciences, Institut Teknologi Bandung
Aerospace Engineering Astronomy Automotive Engineering Chemical Engineering, Chemistry & Bioengineering Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Electrical & Electronics Engineering Engineering Mathematics Physics

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Total vertex irregularity strength for trees with many vertices of degree two Rinovia Simanjuntak; Susilawati Susilawati; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): 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.2020.8.2.17

Abstract

For a simple graph G = (V,E), a mapping φ : V ∪ E → {1,2,...,k} is defined as a vertex irregular total k-labeling of G if for every two different vertices x and y, wt(x) ≠ wt(y), where wt(x) = φ(x)+ Σ????xy∈E(G) φ(xy). The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G. In this paper, we provide three possible values of total vertex irregularity strength for trees with many vertices of degree two. For each of the possible values, sufficient conditions for trees with corresponding total vertex irregularity strength are presented.
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.
The rainbow 2-connectivity of Cartesian products of 2-connected graphs and paths Bety Hayat Susanti; A.N.M. Salman; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 1 (2020): 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.2020.8.1.11

Abstract

An edge-colored graph G is rainbow k-connected, if there are k-internally disjoint rainbow paths connecting every pair of vertices of G. The rainbow k-connection number of G, denoted by rck(G), is the minimum number of colors needed for which there exists a rainbow k-connected coloring for G. In this paper, we are able to find sharp lower and upper bounds for the rainbow 2-connection number of Cartesian products of arbitrary 2-connected graphs and paths. We also determine the rainbow 2-connection number of the Cartesian products of some graphs, i.e. complete graphs, fans, wheels, and cycles, with paths.
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.
Super edge-magic labeling of graphs: deficiency and maximality Anak Agung Gede Ngurah; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 2 (2017): 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.2017.5.2.5

Abstract

A graph G of order p and size q is called super edge-magic if there exists a bijective function f from V(G) U E(G) to {1, 2, 3, ..., p+q} such that f(x) + f(xy) + f(y) is a constant for every edge $xy \in E(G)$ and f(V(G)) = {1, 2, 3, ..., p}. The super edge-magic deficiency of a graph G is either the smallest nonnegative integer n such that G U nK_1 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 graphs. We found a lower bound of the super edge-magic deficiency of join product of any connected graph with isolated vertices and a better upper bound of the super edge-magic deficiency of join product of super edge-magic graphs with isolated vertices. Also, we provide constructions of some maximal graphs, ie. super edge-magic graphs with maximal number of edges.
Total vertex irregularity strength of trees with maximum degree five S. Susilawati; Edy Tri Baskoro; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): 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.2018.6.2.5

Abstract

In 2010, Nurdin, Baskoro, Salman and Gaos conjectured that the total vertex irregularity strength of any tree T is determined only by the number of vertices of degrees 1, 2 and 3 in T. This paper will confirm this conjecture by considering all trees with maximum degree five. Furthermore, we also characterize all such trees having the total vertex irregularity strength either t1, t2 or t3, where $t_{i} = \lceil (1+\sum\sb{j=1}\sp{i}n_{j})/(i+1)\rceil$ and ni is the number of vertices of degree i.
Computing the edge irregularity strengths of chain graphs and the join of two graphs Ali Ahmad; Ashok Gupta; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 1 (2018): 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.2018.6.1.15

Abstract

In computer science, graphs are used in variety of applications directly or indirectly. Especially quantitative labeled graphs have played a vital role in computational linguistics, decision making software tools, coding theory and path determination in networks. For a graph G(V, E) with the vertex set V and the edge set E, a vertex k-labeling ϕ : V → {1, 2, …, k} is defined to be an edge irregular k-labeling of the graph G if for every two different edges e and f their wϕ(e) ≠ wϕ(f), where the weight of an edge e = xy ∈ E(G) is wϕ(xy) = ϕ(x) + ϕ(y). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, denoted by es(G). In this paper, we determine the edge irregularity strengths of some chain graphs and the join of two graphs. We introduce a conjecture and open problems for researchers for further research.
The Uniqueness of Almost Moore Digraphs with Degree 4 And Diameter 2 Rinovia Simanjuntak; Edy Tri Baskoro
Journal of Mathematical and Fundamental Sciences Vol. 32 No. 1 (2000)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Abstract. It is well known that Moore digraphs of degree d > 1 and diameter k > 1 do not exist. For degrees 2 and 3, it has been shown that for diameter k ≥ 3 there are no almost Moore digraphs, i.e. the diregular digraphs of order one less than the Moore bound. Digraphs with order close to the Moore bound arise in the construction of optimal networks. For diameter 2, it is known that almost Moore digraphs exist for any degree because the line digraphs of complete digraphs are examples of such digraphs. However, it is not known whether these are the only almost Moore digraphs. It is shown that for degree 3, there are no almost Moore digraphs of diameter 2 other than the line digraph of K4. In this paper, we shall consider the almost Moore digraphs of diameter 2 and degree 4. We prove that there is exactly one such digraph, namely the line digraph of K5. Ketunggalan Graf Berarah Hampir Moore dengan Derajat 4 dan Diameter 2Sari. Telah lama diketahui bahwa tidak ada graf berarah Moore dengan derajat d>1 dan diameter k>1. Lebih lanjut, untuk derajat 2 dan 3, telah ditunjukkan bahwa untuk diameter t>3, tidak ada graf berarah Hampir Moore, yakni graf berarah teratur dengan orde satu lebih kecil dari batas Moore. Graf berarah dengan orde mendekati batas Moore digunakan dalam pcngkonstruksian jaringan optimal. Untuk diameter 2, diketahui bahwa graf berarah Hampir Moore ada untuk setiap derajat karena graf berarah garis (line digraph) dari graf komplit adalah salah satu contoh dari graf berarah tersebut. Akan tetapi, belum dapat dibuktikan apakah graf berarah tersebut merupakan satu-satunya contoh dari graf berarah Hampir Moore tadi. Selanjutnya telah ditunjukkan bahwa untuk derajat 3, tidak ada graf berarah Hampir Moore diameter 2 selain graf berarah garis dari K4. Pada makalah ini, kita mengkaji graf berarah Hampir Moore diameter 2 dan derajat 4. Kita buktikan bahwa ada tepat satu graf berarah tersebut, yaitu graf berarah garis dari K5.
Multipartite Ramsey numbers for the union of stars I Wayan Palton Anuwiksa; Rinovia Simanjuntak; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.21

Abstract

Let s and k be positive integers with k ≥ 2 and G1, G2, …, Gk be simple graphs. The set multipartite Ramsey number, denoted by Ms(G1, G2, …, Gk), is the smallest positive integer c such that any k-coloring of the edges of Kc × s contains a monochromatic copy of Gi in color i for some i ∈ {1, 2, …, k}. The size multipartite Ramsey number, denoted by mc(G1, G2, …, Gk), is the smallest positive integer s such that any k-coloring of the edges of Kc × s contains a monochromatic copy of Gi in color i for some i ∈ {1, 2, …, k}. In this paper, we establish some lower and upper bounds, and some exact values of multipartite Ramsey numbers for the union of stars.
Distance antimagic labelings of product graphs Risma Yulina Wulandari; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.9

Abstract

A graph G is distance antimagic if there is a bijection f : V(G)→{1, 2, …, |V(G)|} such that for every pair of distinct vertices x and y applies w(x)≠w(y), where w(x)=Σ z ∈ N(x)f(z) and N(x) is the neighbourhood of x, i.e., the set of all vertices adjacent to x. It was conjectured that a graph is distance antimagic if and only if each vertex in the graph has a distinct neighbourhood. In this paper, we study the truth of the conjecture by posing sufficient conditions and constructing distance antimagic product graphs; the products under consideration are join, corona, and Cartesian.
Co-Authors A.N.M. Salman A.N.M. Salman Ali Ahmad Anak Agung Gede Ngurah Anak Agung Gede Ngurah Anam, Juzd Thoha Chairul Andrea Semaničová-Feňovčíková Ashok Gupta Baca, Martin Baskoro, Edy Tri Bety Hayat Susanti Edy Tri Baskoro Faisal Susanto Fawwaz Chirag Sofyan Hassan Pervaiz I Wayan Palton Anuwiksa Kiki A. Sugeng Martin Baca Muchtar, Gatot Mochamad Muzaki, Anggi Afif Nurdin Hinding Pancahayani, Sigit Pancahayani, Sigit Risma Yulina Wulandari Saladin Uttunggadewa Saputro, Suhadi Wido Semanicova-Fenovcıkova, Andrea Suhadi Wido Saputro Susanto, Faisal Susilawati, S. Syafrizal Sy Wulandari, Risma Yulina Yeva Fadhilah Ashari