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All Journal Jurnal Ilmu dan Teknologi Kelautan Tropis JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Electronic Journal of Graph Theory and Applications (EJGTA) Jurnal Matematika & Sains Journal of Mathematical and Fundamental Sciences Indonesian Journal of Combinatorics Makara Journal of Science International Journal of Computing Science and Applied Mathematics-IJCSAM
Denny Riama Silaban
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, Universitas Indonesia
Astronomy Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Electrical & Electronics Engineering Library & Information Science Mathematics Physics

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Vertex-Magic Total Labeling Algorithms on Unicycle Graphs and Some Graphs Related to Wheels Denny Riama Silaban; Budi Utami; Alfa Isti Ananda; Dhian Widya; Siti Aminah
Jurnal Matematika & Sains Vol 17, No 1 (2012)
Publisher : Institut Teknologi Bandung

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Abstract

Abstract Let G be a graph with vertex set V and edge set E, where |V| and |E| be the number of vertices and edges of G. A bijection λ : V È E ® {1, 2, …, |V| + |E|} is called a vertex-magic total labeling if there is a constant k so that the weight of vertex x, wλ(x) = λ(x) + åyÎN(x) λ(xy) = k, for all x in V where N(x) is the set of vertices adjacent to x. This paper gives algorithms to generate all vertex-magic total labelings on some classes of unicycle graphs (suns and tadpoles) and some classes of graph related to wheels (friendships, fans, generalized Jahangirs). Using those algorithms, we enumerate all non isomorphic vertex-magic total labelings on those classes of graphs for some values of |V|.   Keywords: Fan, Friendship, Generalized Jahangir, Sun, Tadpole, Unicycle, Vertex magic total labeling, Wheel.   Algoritma Pelabelan Total Simpul Ajaib pada Graf Unicyle dan Beberapa Graf yang Terkait dengan Roda Abstrak Misalkan G adalah graf dengan himpunan simpul V dan himpunan busur  E dengan |V| dan |E| menyatakan banyak simpul dan banyak busur pada G. Fungsi bijektif  λ : V È E ® {1, 2, …, |V| + |E|} disebut pelabelan total simpul ajaib jika ada konstanta k sedemikian sehingga bobot simpul x, wλ(x) = λ(x) + åyÎN(x) λ(xy) = k, untuk setiap x di V dengan N(x) menyatakan, himpunan simpul yang berdekatan dengan x. Makalah ini memberikan algoritma-algoritma untuk menghasikan semua pelabelan-pelabelan  total simpul ajaib pada beberapa kelas graf unicycle (matahari dan kecebong) dan beberapa kelas graf yang terkait dengan roda (friendship, kipas, generalized Jahangir). Menggunakan algoritma-algoritma tersebut, dienumerasi semua pelabelan total simpul ajaib yang tidak isomorfik pada kelas-kelas graf yang menjadi perhatian, untuk beberapa nilai dari |V|. Kata kunci: Friendship, Generalized Jahangir, Kecebong, Kipas, Matahari, Pelabelan total simpul ajaib, Unicycle. 
Restricted size Ramsey number for path of order three versus graph of order five Denny Riama Silaban; Edy Tri Baskoro; Saladin Uttunggadewa
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 1 (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.2017.5.1.15

Abstract

Let $G$ and $H$ be simple graphs. The Ramsey number for a pair of graph $G$ and $H$ is the smallest number $r$ such that any red-blue coloring of edges of $K_r$ contains a red subgraph $G$ or a blue subgraph $H$. The size Ramsey number for a pair of graph $G$ and $H$ is the smallest number $\hat{r}$ such that there exists a graph $F$ with size $\hat{r}$ satisfying the property that any red-blue coloring of edges of $F$ contains a red subgraph $G$ or a blue subgraph $H$. Additionally, if the order of $F$ in the size Ramsey number is $r(G,H)$, then it is called the restricted size Ramsey number. In 1983, Harary and Miller started to find the (restricted) size Ramsey number for any pair of small graphs with order at most four. Faudree and Sheehan (1983) continued Harary and Miller's works and summarized the complete results on the (restricted) size Ramsey number for any pair of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for any pair of small forests with order at most five. To continue their works, we investigate the restricted size Ramsey number for a path of order three versus connected graph of order five.
On the restricted size Ramsey number for P3 versus dense connected graphs Denny Riama Silaban; Edy Tri Baskoro; Saladin Uttunggadewa
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.2020.8.2.14

Abstract

Let F, G and H be simple graphs. A graph F is said a (G,H)-arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H. The size Ramsey number of G and H, ŕ(G,H), is the minimum size of F. If the order of F equals to the Ramsey number of G and H, r(G,H), then the minimum size of F is called the restricted size Ramsey number of G and H, r*(G,H). The Ramsey number of G and H, r(G,H), is the minimum order of F. In this paper, we study the restricted size number involving a P3.  The value of r*(P3,Kn) has been given by Faudree and Sheehan. Here, we examine r*(P3,H) where H is dense connected graph.
Restricted Size Ramsey Number Involving Matching and Graph of Order Five Denny Riama Silaban; Edy Tri Baskoro; Saladin Uttunggadewa
Journal of Mathematical and Fundamental Sciences Vol. 52 No. 2 (2020)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2020.52.2.1

Abstract

Harary and Miller (1983) started the research on the (restricted) size Ramsey number for a pair of small graphs. They obtained the values for some pairs of small graphs with order not more than four. In the same year, Faudree and Sheehan continued the research and extended the result to all pairs of small graphs with order not more than four. Moreover, in 1998, Lortz and Mengenser gave the size Ramsey number and the restricted size Ramsey number for all pairs of small forests with order not more than five. Recently, we gave the restricted size Ramsey number for a path of order three and any connected graph of order five. In this paper, we continue the research on the (restricted) size Ramsey number involving small graphs by investigating the restricted size Ramsey number for matching with two edges versus any graph of order five with no isolates.
Super local edge anti-magic total coloring of paths and its derivation Fawwaz Fakhrurrozi Hadiputra; Denny Riama Silaban; Tita Khalis Maryati
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (636.8 KB) | DOI: 10.19184/ijc.2019.3.2.6

Abstract

Suppose G(V,E) be a connected simple graph and suppose u,v,x be vertices of graph G. A bijection f : V ∪ E → {1,2,3,...,|V (G)| + |E(G)|} is called super local edge antimagic total labeling if for any adjacent edges uv and vx, w(uv) 6= w(vx), which w(uv) = f(u)+f(uv)+f(v) for every vertex u,v,x in G, and f(u) < f(e) for every vertex u and edge e ∈ E(G). Let γ(G) is the chromatic number of edge coloring of a graph G. By giving G a labeling of f, we denotes the minimum weight of edges needed in G as γleat(G). If every labels for vertices is smaller than its edges, then it is be considered γsleat(G). In this study, we proved the γ sleat of paths and its derivation.
On local antimagic vertex coloring of corona products related to friendship and fan graph Zein Rasyid Himami; Denny Riama Silaban
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.7

Abstract

Let G=(V,E) be connected graph. A bijection f : E → {1,2,3,..., |E|} is a local antimagic of G if any adjacent vertices u,v ∈ V satisfies w(u)≠ w(v), where w(u)=∑e∈E(u) f(e), E(u) is the set of edges incident to u. When vertex u is assigned the color w(u), we called it a local antimagic vertex coloring of G. A local antimagic chromatic number of G, denoted by χla(G), is the minimum number of colors taken over all colorings induced by the local antimagic labeling of G. In this paper, we determine the local antimagic chromatic number of corona product of friendship and fan with null graph on m vertices, namely, χla(Fn ⊙ \overline{K_m}) and χla(f(1,n) ⊙ \overline{K_m}).
On b-edge consecutive edge magic total labeling on trees Eunike Setiawan; Kiki Ariyanti Sugeng; Denny Riama Silaban
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.2022.10.2.15

Abstract

Let G = (V, E) be a simple, connected, and undirected graph, where V and E are the set of vertices and the set of edges of G. An edge magic total labeling on G is a bijection f : V ∪ E → {1, 2, …, |V|+|E|}, provided that for every uv ∈ E, w(uv)=f(u)+f(v)+f(uv)=K for a constant number K. Such a labeling is said to be a super edge magic total labeling if f(V)={1,2,…,|V|} and a b-edge consecutive edge magic total labeling if f(E)={b+1,b+2,…,b+|E|} with b ≥ 1. In this research, we give sufficient conditions for a graph G having a super edge magic total labeling to have a b-edge consecutive edge magic total labeling. We also give several classes of connected graphs which have both labelings.
Further results on local inclusive distance vertex irregularity strength of graphs Fawwaz Fakhrurrozi Hadiputra; Eunike Setiawan; Tita Khalis Maryati; Denny Riama Silaban
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.2023.11.1.21

Abstract

Let G = (V, E) be a simple undirected graph. A labeling f : V(G)→{1, …, k} is a local inclusive d-distance vertex irregular labeling of G if every adjacent vertices x, y ∈ V(G) have distinct weights, with the weight w(x),x ∈ V(G) is the sum of every labels of vertices whose distance from x is at most d. The local inclusive d-distance vertex irregularity strength of G, lidis(G), is the least number k for which there exists a local inclusive d-distance vertex irregular labeling of G. In this paper, we prove a conjecture on the local inclusive d-distance vertex irregularity strength for d = 1 for tree and we generalize the result for block graph using the clique number. Furthermore, we present several results for multipartite graphs and we also observe the relationship with chromatic number.
PENGEMBANGAN PERANGKAT LUNAK SIMULASI KOMPUTER SEBAGAI ALAT BANTU DALAM ANALISIS FARMAKOKINETIK Handari, Bevina D; Djajadisastra, Joshita; Silaban, Denny Riama
Makara Journal of Science Vol. 10, No. 1
Publisher : UI Scholars Hub

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Abstract

The Development of a Computer Simulation Software as a Tool in Pharmacokinetics Analisys. This research uses mammilary model (one compartment and two compartments) as compartment model in which a single drug administration is given via oral and intravenous. Mathematical modeling in differential equations can be derived from a pharmacokinetics model. The solutions are pharmacokinetics variables and parameters that can be solved using some mathematical and numerical methods such as Laplace transformation, residual method, superposition principle, trapezoidal rule and some solving methods in differential equations.To overcome manual calculation and to visualize a drug’s dynamics in the graph form, a computer simulation software based on Visual Basic has been built. The simulation results show that any particular sample data plasma can be checked whether it is given orally or injection and has a tendency to be compatible with an assumption of one compartment or two compartments. For urin data, the software capability is still limited only for one compartment. However, it can checked if the corresponding data is given via oral or injection. So the simulations show that pharmacokinetics variables and parameters will have individual effects
Spectral Characteristics of The Antiadjacency Matrix of Kite Graph Miming Fikria Camilla; Melza Rensiana; Denny Riama Silaban
Jurnal Matematika, Statistika dan Komputasi Vol. 21 No. 2 (2025): JANUARY 2025
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v21i2.40490

Abstract

Let G=(V,E)  be a connected graph, where V is the set of vertices and E is the set of edges of G. The kite graph, denoted by Kiten,m, is a graph obtained by appending a complete graph Kn to a pendant vertex of path Pm. This research investigates the spectrum of antiadjacency matrix of kite graph. The antiadjacency matrix of a graph G of order n is a square matrix with order n where the entries of the matrix represent the nonadjacency of the vertices.  
Co-Authors Alfa Isti Ananda Bevina D Handari Budi Utami Chandra, Ivana Joice Chandra, Ivana Joice Dhian Widya Edy Tri Baskoro Elda Safitri Elda Safitri Eunike Setiawan Eunike Setiawan Fauziah, Yasmin Fawwaz Fakhrurrozi Hadiputra Fawwaz Fakhrurrozi Hadiputra Joshita Djajadisastra Joshita Djajadisastra, Joshita Kiki Ariyanti Sugeng Koesratmoko, Eko Melza Rensiana Miming Fikria Camilla Mufti Petala Patria Nurfata, Azzahra Shinta Bilqis Peter John Peter John Saladin Uttunggadewa Siti Aminah Tika, Nurhasanah Tita Khalis Maryati Walfried, Yosua Zein Rasyid Himami