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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 Total Edge Irregular Strengths of Union Graphs of K2,n Nurdin Nurdin; Edy Tri Baskoro; Muhammad Salman Alfarisi Nawawi
Jurnal Matematika & Sains Vol 11, No 3 (2006)
Publisher : Institut Teknologi Bandung

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

Abstract

For a simple graph G = (V, E) with the vertex setV and the edge setV, a labeling l :V ÈE ® {1,2,...,k} is called an edge irregular total k-labelling of G if for any two different edges  e = e e1 e e2 and  f = f1 f2 in E (G) we have wt (e) wt (f ) where (e) = l (e1) + l (e ) + l (e2 ). The total edge irregular strengths tes (G) of G is the smallest positive integer k for which G has an edge irregular total k-labelling. In this paper, a dual of an edge irregular total klabelling is introduced. Beside that, the total edge irregular strengths of a graph mK2,n -path and a graph mK2,n for any positive integer m ≥  1 and n ≥ 2 have been determined.
APPLYING THE APOS THEORY TO IMPROVE STUDENTS ABILITY TO PROVE IN ELEMENTARY ABSTRACT ALGEBRA Arnawa, I Made; sumarno, Utari; Kartasasmita, Bana; Baskoro, Edy Tri
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 Salindeho, Brilly Maxel; Assiyatun, Hilda; Baskoro, Edy Tri
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.
On size multipartite Ramsey numbers for stars versus paths and cycles Anie Lusiani; Edy Tri Baskoro; Suhadi Wido Saputro
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.2017.5.1.5

Abstract

Let $K_{l\times t}$ be a complete, balanced, multipartite graph consisting of $l$ partite sets and $t$ vertices in each partite set. For given two graphs $G_1$ and $G_2$, and integer $j\geq 2$, the size multipartite Ramsey number $m_j(G_1,G_2)$ is the smallest integer $t$ such that every factorization of the graph $K_{j\times t}:=F_1\oplus F_2$ satisfies the following condition: either $F_1$ contains $G_1$ or $F_2$ contains $G_2$. In 2007, Syafrizal et al. determined the size multipartite Ramsey numbers of paths $P_n$ versus stars, for $n=2,3$ only. Furthermore, Surahmat et al. (2014) gave the size tripartite Ramsey numbers of paths $P_n$ versus stars, for $n=3,4,5,6$. In this paper, we investigate the size tripartite Ramsey numbers of paths $P_n$ versus stars, with all $n\geq 2$. Our results complete the previous results given by Syafrizal et al. and Surahmat et al. We also determine the size bipartite Ramsey numbers $m_2(K_{1,m},C_n)$ of stars versus cycles, for $n\geq 3,m\geq 2$.
The connected size Ramsey number for matchings versus small disconnected graphs Hilda Assiyatun; Budi Rahadjeng; Edy Tri Baskoro
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.2019.7.1.9

Abstract

Let F, G,  and H be simple graphs. The notation F → (G, H) means that if all the edges of F are arbitrarily colored by red or blue, then there always exists either a red subgraph G or a blue subgraph H. The size Ramsey number of graph G and H,  denoted by r̂(G, H) is the smallest integer k such that there is a graph F with k edges satisfying F → (G, H). In this research, we will study a modified size Ramsey number, namely the connected size Ramsey number. In this case, we only consider connected graphs F satisfying the above properties. This connected size Ramsey number of G and H is denoted by r̂c(G, H). We will derive an upper bound of r̂c(nK2, H), n ≥ 2 where H is 2Pm or 2K1, t,  and find the exact values of r̂c(nK2, H),  for some fixed n.
Determining finite connected graphs along the quadratic embedding constants of paths Edy Tri Baskoro; Nobuaki Obata
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (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.2021.9.2.23

Abstract

The QE constant of a finite connected graph G, denoted by QEC(G), is by definition the maximum of the quadratic function associated to the distance matrix on a certain sphere of codimension two. We prove that the QE constants of paths Pn form a strictly increasing sequence converging to −1/2. Then we formulate the problem of determining all the graphs G satisfying QEC(Pn)≤QEC(G)<QEC(Pn + 1). The answer is given for n = 2 and n = 3 by exploiting forbidden subgraphs for QEC(G)< − 1/2 and the explicit QE constants of star products of the complete graphs.
Size multipartite Ramsey numbers for stripes versus small cycles Chula Janak Jayawardene; Edy Tri Baskoro; Lilanthi Samarasekara; Syafrizal Sy
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (2016): 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.2016.4.2.4

Abstract

For simple graphs $G_1$ and $G_2$, the size Ramsey multipartite number $m_j(G_1, G_2)$ is defined as the smallest natural number $s$ such that any arbitrary two coloring of the graph $K_{j \times s}$ using the colors red and blue, contains a red $G_1$ or a blue $G_2$ as subgraphs. In this paper, we obtain the exact values of the size Ramsey numbers $m_j(nK_2, C_m)$ for $j \ge 2$ and $m \in \{3,4,5,6\}$.
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.
Characterizing all trees with locating-chromatic number 3 Edy Tri Baskoro; A Asmiati
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 1, No 2 (2013): 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.2013.1.2.4

Abstract

Let $c$ be a proper $k$-coloring of a connected graph $G$.  Let $\Pi = \{S_{1}, S_{2},\ldots, S_{k}\}$ be the induced  partition of $V(G)$ by $c$,  where $S_{i}$ is the partition class having all vertices with color $i$.The color code $c_{\Pi}(v)$ of vertex $v$ is the ordered$k$-tuple $(d(v,S_{1}), d(v,S_{2}),\ldots, d(v,S_{k}))$, where$d(v,S_{i})= \hbox{min}\{d(v,x)|x \in S_{i}\}$, for $1\leq i\leq k$.If all vertices of $G$ have distinct color codes, then $c$ iscalled a locating-coloring of $G$.The locating-chromatic number of $G$, denoted by $\chi_{L}(G)$, isthe smallest $k$ such that $G$ posses a locating $k$-coloring. Clearly, any graph of order $n \geq 2$ have locating-chromatic number $k$, where $2 \leq k \leq n$. Characterizing all graphswith a certain locating-chromatic number is a difficult problem. Up to now, we have known allgraphs of order $n$ with locating chromatic number $2, n-1,$ or $n$.In this paper, we characterize all trees whose locating-chromatic number $3$. We also give a family of trees with locating-chromatic number 4.
On 2-power unicyclic cubic graphs Shariefuddin Pirzada; Mushtaq Shah; 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.2022.10.1.24

Abstract

In a graph, a cycle whose length is a power of two (that is, 2k) is called a 2-power cycle. In this paper, we show that the existence of an infinite family of cubic graphs which contain only one cycle whose length is a power of 2. Such graphs are called as 2-power unicyclic cubic graphs. Further we observe that the only 2-power cycle in a cubic graph cannot be removed implying that there does not exist a counter example for Erdos-Gyárfás conjecture.
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