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Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia

Published : 8 Documents
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Characterizing all trees with locating-chromatic number 3 Baskoro, Edy Tri; Asmiati, A
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

#### Abstract

Let \$c\$ be a proper \$k\$-coloring of a connected graph \$G\$.Â Â Let \$Pi = {S_{1}, S_{2},ldots, S_{k}}\$ be the inducedÂ Â partition of \$V(G)\$ by \$c\$,Â Â 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 \$1leq ileq 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.
The Uniqueness of Almost Moore Digraphs with Degree 4 And Diameter 2 Simanjuntak, Rinovia; Baskoro, Edy Tri
Journal of Mathematical and Fundamental Sciences Vol 32, No 1 (2000)
Publisher : ITB Journal Publisher, LPPM ITB

#### Abstract

Abstract. It is well known that Moore digraphs of degree d &gt; 1 and diameter k &gt; 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&gt;1 dan diameter k&gt;1. Lebih lanjut, untuk derajat 2 dan 3, telah ditunjukkan bahwa untuk diameter t&gt;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.
BILANGAN RAMSEY SISI DARI r(P3,Pn) Imron, Chairul; Baskoro, Edy Tri
Berkala Ilmiah MIPA Vol 16, No 2 (2006)
Publisher : FMIPA UGM

#### Abstract

Pada paper ini akan ditunjukkan bahwa bilangan Ramsey sisi dari r(P3,Pn) untuk n = 13, 14, 15 adalah 20, 23, 24. Ditunjukkan pula bahwa r(P3,pn)=r(P3,Pk)+r(P3,P1) dengan n = k+l-1 untuk n ganjil dan k, l genap. Kata kunci: Bilangan Ramsey sisi, Graph lintasan
The complete list of Ramsey \$(2K_2,K_4)\$-minimal graphs Wijaya, Kristiana; Baskoro, Edy Tri; Assiyatun, Hilda; Suprijanto, Djoko
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

#### Abstract

Let \$F, G,\$ and \$H\$ be non-empty graphs. The notation \$F ightarrow (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 ightarrow (G,H)\$ and \$(F-e) rightarrow (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.
Trees with Certain Locating-chromatic Number Syofyan, Dian Kastika; Baskoro, Edy Tri; Assiyatun, Hilda
Journal of Mathematical and Fundamental Sciences Vol 48, No 1 (2016)
Publisher : ITB Journal Publisher, LPPM ITB

#### Abstract

The locating-chromatic number of a graph G can be defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are not contained in the same partition class. In this case, the coordinate of a vertex v in G is expressed in terms of the distances of v to all partition classes. This concept is a special case of the graph partition dimension notion. Previous authors have characterized all graphs of order n with locating-chromatic number either n or n-1. They also proved that there exists a tree of order n, nâ¥5, having locating-chromatic number k if and only if kÂ â{3,4,â¦,n-2,n}. In this paper, we characterize all trees of order n with locating-chromatic number n - t, for any integers n and t, where nÂ &gt; t+3 and 2 â¤ t &lt; n/2.
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

#### 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 :Â http://dx.doi.org/10.22342/jims.13.1.80.133-148
On the Ramsey number of 4-cycle versus wheel Noviani, Enik; Baskoro, Edy Tri
Indonesian Journal of Combinatorics Vol 1, No 1 (2016)
Publisher : Indonesian Combinatorial Society (InaCombS)

#### Abstract

For any fixed graphs \$G\$ and \$H\$, the Ramsey number \$R(G,H)\$ is the smallest positive integer \$n\$ such that for every graph \$F\$ on \$n\$ vertices must contain \$G\$ or the complement of \$F\$ contains \$H\$. The girth of graph \$G\$ is a length of the shortest cycle. A \$k\$-regular graph with the girth \$g\$ is called a \$(k,g)\$-graph. If the number of of vertices in \$(k,g)\$-graph is minimized then we call this graph a \$(k,g)\$-cage. In this paper, we derive the bounds of Ramsey number \$R(C_4,W_n)\$ for some values of \$n\$. By modifying \$(k, 5)\$-graphs, for \$k = 7\$ or \$9\$, we construct these corresponding \$(C_4,W_n)\$-good graphs.
The connected size Ramsey number for matchings versus small disconnected graphs Assiyatun, Hilda; Rahadjeng, Budi; Baskoro, Edy Tri
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

#### 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.