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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) Journal of the Indonesian Mathematical Society Jurnal Matematika & Sains Journal of Mathematical and Fundamental Sciences Indonesian Journal of Combinatorics
Edy Tri Baskoro
Institut Teknologi Bandung
Astronomy Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Electrical & Electronics Engineering Mathematics Physics

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The complete list of Ramsey $(2K_2,K_4)$-minimal graphs Kristiana Wijaya; Edy Tri Baskoro; Hilda Assiyatun; Djoko Suprijanto
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 2 (2015): 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.2015.3.2.9

Abstract

Let $F, G,$ and $H$ be non-empty graphs. The notation $F \rightarrow (G,H)$ means that if all edges of $F$ are arbitrarily colored by red or blue, then either the subgraph of $F$ induced by all red edges contains a graph $G$ or the subgraph of $F$ induced by all blue edges contains a graph $H.$ A graph $F$ satisfying two conditions: $F \rightarrow (G,H)$ and $(F-e) \nrightarrow (G,H)$ for every $e \in E(F)$ is called a Ramsey $(G,H)-$minimal graph. In this paper, we determine all non-isomorphic Ramsey $(2K_2,K_4)$-minimal graphs.
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.
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.
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.
Ramsey minimal graphs for a pair of a cycle on four vertices and an arbitrary star Maya Nabila; Hilda Assiyatun; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (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.2022.10.1.20

Abstract

Let F, G and H be simple graphs. The notation F → (G, H) means that for any red-blue coloring on the edges of graph F, there exists either a red copy of G or a blue copy of H. A graph F is called a Ramsey (G, H)-minimal graph if it satisfies two conditions: (i) F → (G, H) and (ii) F − e ↛ (G, H) for any edge e of F. In this paper, we give some finite and infinite classes of Ramsey (C4, K1, n)-minimal graphs for any n ≥ 3.
On energy, Laplacian energy and $p$-fold graphs Hilal A Ganie; Shariefuddin Pirzada; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 1 (2015): 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.2015.3.1.10

Abstract

For a graph $G$ having adjacency spectrum ($A$-spectrum) $\lambda_n\leq\lambda_{n-1}\leq\cdots\leq\lambda_1$ and Laplacian spectrum ($L$-spectrum) $0=\mu_n\leq\mu_{n-1}\leq\cdots\leq\mu_1$, the energy is defined as $ E(G)=\sum_{i=1}^{n}|\lambda_i|$ and the Laplacian energy is defined as $LE(G)=\sum_{i=1}^{n}|\mu_i-\frac{2m}{n}|$. In this paper, we give upper and lower bounds for the energy of $KK_n^j,~1\leq j \leq n$ and as a consequence we generalize a result of Stevanovic et al. [More on the relation between Energy and Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. {\bf 61} (2009) 395-401]. We also consider strong double graph and strong $p$-fold graph to construct some new families of graphs $G$ for which $E(G)> LE(G)$.
A method to construct graphs with certain partition dimension Debi Oktia Haryeni; Edy Tri Baskoro; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (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.2019.7.2.5

Abstract

In this paper, we propose a method for constructing new graphs from a given graph G so that the resulting graphs have the partition dimension at most one larger than the partition dimension of the graph G. In particular, we employ this method to construct a family of graphs with partition dimension 3.
APPLYING THE APOS THEORY TO IMPROVE STUDENTS ABILITY TO PROVE IN ELEMENTARY ABSTRACT ALGEBRA I Made Arnawa; Utari sumarno; Bana Kartasasmita; Edy Tri Baskoro
Journal of the Indonesian Mathematical Society Volume 13 Number 1 (April 2007)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.13.1.80.133-148

Abstract

This study is a quasi-experimental nonrandomized pretest-posttest control group design. The experiment group is treated by APOS theory instruction (APOS),that implements four characteristics of APOS theory, (1) mathematical knowledge was constructed through mental construction: actions, processes, objects, and organizing these in schemas, (2) using computer, (3) using cooperative learning groups, and (4) using ACE teaching cycle (activities, class discussion, and exercise). The control group is treated by conventional/traditional mathematics instruction (TRAD). The main purpose of this study is to analyze about achievement in proof. 180 students from two different universities (two classes at the Department of Mathematics UNAND and two classes atthe Department of Mathematics Education UNP PADANG) were engaged as the research subjects. Based on the result of data analysis, the main result of this study is that the proof ability of students' in the APOS group is significantly better than student in TRAD group, so it is strongly suggested to apply APOS theory in Abstract Algebra course.DOA : http://dx.doi.org/10.22342/jims.13.1.80.133-148
On The Locating-Chromatic Numbers of Subdivisions of Friendship Graph Brilly Maxel Salindeho; Hilda Assiyatun; Edy Tri Baskoro
Journal of the Indonesian Mathematical Society Volume 26 Number 2 (July 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.2.822.175-184

Abstract

Let c be a k-coloring of a connected graph G and let pi={C1,C2,...,Ck} be the partition of V(G) induced by c. For every vertex v of G, let c_pi(v) be the coordinate of v relative to pi, that is c_pi(v)=(d(v,C1 ),d(v,C2 ),...,d(v,Ck )), where d(v,Ci )=min{d(v,x)|x in Ci }. If every two vertices of G have different coordinates relative to pi, then c is said to be a locating k-coloring of G. The locating-chromatic number of G, denoted by chi_L (G), is the least k such that there exists a locating k-coloring of G. In this paper, we determine the locating-chromatic numbers of some subdivisions of the friendship graph Fr_t, that is the graph obtained by joining t copies of 3-cycle with a common vertex, and we give lower bounds to the locating-chromatic numbers of few other subdivisions of Fr_t.
Total Edge Irregularity Strength of the Disjoint Union of Helm Graphs Muhammad Kamran Siddiqui; N. Nurdin; Edy Tri Baskoro
Journal of Mathematical and Fundamental Sciences Vol. 45 No. 2 (2013)
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.2013.45.2.6

Abstract

The total edge irregular k-labeling of a graph G=(V,E) is the labeling of vertices and edges of G in such a way that for any different edges their weights are distinct. The total edge irregularity strength, tes (G), is defined as the minimum k for which G has a total edge irregular k-labeling. In this paper, we consider the total edge irregularity strength of the disjoint union of m special types of helm graphs.
Co-Authors A Asmiati Ahmad Erfanian Anisa Rarasati Arfin Arfin Bana Kartasasmita Bana Kartasasmita Brilly Maxel Salindeho BUDI RAHADJENG Chula Janak Jayawardene Debi Oktia Haryeni Debi Oktia Haryeni Debi Oktia Haryeni Denny Riama Silaban Denny Riama Silaban Dian Kastika Syofyan Dian Kastika Syofyan Dinny Fitriani Djoko Suprijanto Enik Noviani Erfanian, Ahmad Faisal Susanto Gholamreza Abrishami Gregory Benedict Tanidi Hilal A Ganie Hilda Assiyatun Hilda Assiyatun Hilda Assiyatun Hilda Assiyatun Hilda Assiyatun Hilda Assiyatun Hilda Assiyatun Hilda Assiyatun, Hilda I Made Arnawa I Made Arnawa I Wayan Palton Anuwiksa Josef Siran Korivand, Meysam Kristiana Wijaya Lilanthi Samarasekara Lusiani, Anie Maya Nabila Maya Nabila Meysam Korivand Mirka Miller Mojdeh, Doost Ali Mostafa Tavakoli Muhammad Kamran Siddiqui Muhammad Ridwan Muhammad Salman Alfarisi Nawawi Mushtaq Shah N. Nurdin Nobuaki Obata Nurdin Nurdin Ratih Suryaningsih Rika Yanti Rinovia Simanjuntak Rinovia Simanjuntak Rinovia Simanjuntak Rinovia Simanjuntak Rinovia Simanjuntak Saladin Uttunggadewa Saladin Uttunggadewa Saladin Uttunggadewa Salindeho, Brilly Maxel Shariefuddin Pirzada Shariefuddin Pirzada Suhadi Wido Saputro Suhadi Wido Saputro Suhadi Wido Saputro Suhadi Wido Saputro Suhadi Wido Saputro Suhadi Wido Saputro Susilawati, S. Syafrizal Sy Utari sumarno Utari sumarno