Indonesian Journal of Combinatorics最新文献

{"title":"Triangles in the suborbital graphs of the normalizer of $Gamma_0(N)$","authors":"Nazlı Yazıcı Gözütok, B. Ö. Güler","doi":"10.19184/IJC.2020.4.2.1","DOIUrl":"https://doi.org/10.19184/IJC.2020.4.2.1","url":null,"abstract":"<p>In this paper, we investigate a suborbital graph for the normalizer of Γ_{0(<em>N</em>)} ∈ PSL(2;<em>R</em>), where <em>N</em> will be of the form 2⁴<em>p</em>² such that <em>p</em> > 3 is a prime number. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"125 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79207062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Locating-chromatic number of the edge-amalgamation of trees","authors":"Dian Kastika Syofyan, E. Baskoro, H. Assiyatun","doi":"10.19184/IJC.2020.4.2.6","DOIUrl":"https://doi.org/10.19184/IJC.2020.4.2.6","url":null,"abstract":"<div class=\"page\" title=\"Page 1\"><div class=\"layoutArea\"><div class=\"column\"><p><span>The investigation on the locating-chromatic number of a graph was initiated by Chartrand </span><span>et al. </span><span>(2002). This concept is in fact a special case of the partition dimension of a graph. This topic has received much attention. However, the results are still far from satisfaction. We can define the locating-chromatic number of a graph </span><span>G </span><span>as the smallest integer </span><span>k </span><span>such that there exists a </span><span>k</span><span>-partition of the vertex-set of </span><span>G </span><span>such that all vertices have distinct coordinates with respect to this partition. As we know that the metric dimension of a tree is completely solved. However, the locating-chromatic numbers for most of trees are still open. For </span><span><em>i</em> </span><span>= 1</span><span>, </span><span>2</span><span>, . . . , <em>t</em>, </span><span>let </span><em>T</em><span>i </span><span>be a tree with a fixed edge </span><span>e</span><span>o</span><span>i </span><span>called the terminal edge. The edge-amalgamation of all </span><span>T</span><span>i</span><span>s </span><span>denoted by Edge-Amal</span><span>{</span><span>T</span><span>i</span><span>;</span><span>e</span><span>o</span><span>i</span><span>} </span><span>is a tree formed by taking all the </span><span>T</span><span>i</span><span>s and identifying their terminal edges. In this paper, we study the locating-chromatic number of the edge-amalgamation of arbitrary trees. We give lower and upper bounds for their locating-chromatic numbers and show that the bounds are tight.</span></p></div></div></div>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78086923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On (a,d)-antimagic labelings of Hn, FLn and mCn","authors":"Ramalakshmi Rajendran, K. Kathiresan","doi":"10.19184/IJC.2020.4.2.3","DOIUrl":"https://doi.org/10.19184/IJC.2020.4.2.3","url":null,"abstract":"In this paper, we derive the necessary condition for an (a,d )- antimagic labeling of some new classes of graphs such as <em>H</em><em>_n, F L_n </em>and <em>mC</em><em>_n</em>. We prove that <em>H</em><em>_n </em>is (7<em>n </em>+2<em>, </em>1)-antimagic and <em>mC</em><em>_n </em>is ((mn+3)/2,1)- antimagic. Also we prove that <em>F L</em><em>_n </em>has no ((n+1)/2,4)- antimagic labeling.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75320240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New families of star-supermagic graphs","authors":"A. Ngurah","doi":"10.19184/IJC.2020.4.2.4","DOIUrl":"https://doi.org/10.19184/IJC.2020.4.2.4","url":null,"abstract":"A simple graph <em>G</em> admits a <em>K</em>_1,n-covering if every edge in <em>E</em>(<em>G</em>) belongs to a subgraph of <em>G</em> isomorphic to <em>K</em>_1,n. The graph <em>G</em> is <em>K</em>_1,n-supermagic if there exists  a bijection <em>f</em> : <em>V</em>(<em>G</em>) ∪ <em>E</em>(<em>G</em>) → {1, 2, 3,..., |<em>V</em>(<em>G</em>) ∪ <em>E</em>(<em>G</em>)|} such that for every subgraph <em>H</em>' of <em>G</em> isomorphic to <em>K</em>_1,n,  ∑v_{∈ V(H')} f(v) + ∑_{e ∈ E(H')} f(e) is  a constant and <em>f</em>(<em>V</em>(<em>G</em>)) = {1, 2, 3,..., |<em>V</em>(<em>G</em>)|}. In such a case, <em>f</em> is called a <em>K</em>_1,n-supermagic labeling of <em>G</em>.  In this paper, we give a method how to construct <em>K</em>_1,n-supermagic graphs from the old ones.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75209362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On size multipartite Ramsey numbers for stars","authors":"Anie Lusiani, E. Baskoro, S. Saputro","doi":"10.19184/ijc.2019.3.2.4","DOIUrl":"https://doi.org/10.19184/ijc.2019.3.2.4","url":null,"abstract":"<p>Burger and Vuuren defined the size multipartite Ramsey number for a pair of complete, balanced, multipartite graphs <em>mj</em>(<em>Ka</em>x<em>b</em>,<em>Kc</em>x<em>d</em>), for natural numbers <em>a,b,c,d</em> and <em>j</em>, where <em>a,c</em> >= 2, in 2004. They have also determined the necessary and sufficient conditions for the existence of size multipartite Ramsey numbers <em>mj</em>(<em>Ka</em>x<em>b</em>,<em>Kc</em>x<em>d</em>). Syafrizal <em>et al</em>. generalized this definition by removing the completeness requirement. For simple graphs <em>G</em> and <em>H</em>, they defined the size multipartite Ramsey number <em>mj</em>(<em>G,H</em>) as the smallest natural number <em>t</em> such that any red-blue coloring on the edges of <em>Kj</em>x<em>t</em> contains a red <em>G</em> or a blue <em>H</em> as a subgraph. In this paper, we determine the necessary and sufficient conditions for the existence of multipartite Ramsey numbers <em>mj</em>(<em>G,H</em>), where both <em>G</em> and <em>H</em> are non complete graphs. Furthermore, we determine the exact values of the size multipartite Ramsey numbers <em>mj</em>(<em>K</em>1,<em>m</em>, <em>K</em>1,<em>n</em>) for all integers <em>m,n >= </em>1 and <em>j </em>= 2,3, where <em>K</em>1,<em>m</em> is a star of order <em>m</em>+1. In addition, we also determine the lower bound of <em>m</em>3(<em>kK</em>1,<em>m</em>, <em>C</em>3), where <em>kK</em>1,<em>m</em> is a disjoint union of <em>k</em> copies of a star <em>K</em>1,<em>m</em> and <em>C</em>3 is a cycle of order 3.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81033935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Decomposition of complete graphs into connected unicyclic graphs with eight edges and pentagon","authors":"D. Froncek, O'Neill Kingston","doi":"10.19184/IJC.2019.3.1.3","DOIUrl":"https://doi.org/10.19184/IJC.2019.3.1.3","url":null,"abstract":"<p>A <span class=\"math\"><em>G</em></span>-decomposition of the complete graph <span class=\"math\"><em>K</em>_<em>n</em></span> is a family of pairwise edge disjoint subgraphs of <span class=\"math\"><em>K</em>_<em>n</em></span>, all isomorphic to <span class=\"math\"><em>G</em></span>, such that every edge of <span class=\"math\"><em>K</em>_<em>n</em></span> belongs to exactly one copy of <span class=\"math\"><em>G</em></span>. Using standard decomposition techniques based on <span class=\"math\"><em>ρ</em></span>-labelings, introduced by Rosa in 1967, and their modifications we show that each of the ten non-isomorphic connected unicyclic graphs with eight edges containing the pentagon decomposes the complete graph <span class=\"math\"><em>K</em>_<em>n</em></span> whenever the necessary conditions are satisfied.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87524510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Implementation of super H-antimagic total graph on establishing stream cipher","authors":"A. C. Prihandoko, D. Dafik, I. H. Agustin","doi":"10.19184/IJC.2019.3.1.2","DOIUrl":"https://doi.org/10.19184/IJC.2019.3.1.2","url":null,"abstract":"This paper is aimed to study the use of super (a, d)-H antimagic total graph on generating encryption keys that can be used to establish a stream cipher. Methodology to achieve this goal was undertaken in three steps. First of all the existence of super (a, d)-H-antimagic total labeling was proven. At the second step, the algorithm for utilizing the labeling to construct a key stream was developed, and finally, the mechanism for applying the key to establish a stream cipher was constructed. As the result, according to the security analysis, it can be shown that the developed cryptographic system achieve a good security.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75330253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The oriented chromatic number of edge-amalgamation of cycle graph","authors":"D. E. Nurvazly, J. M. Manulang, K. Sugeng","doi":"10.19184/IJC.2019.3.1.5","DOIUrl":"https://doi.org/10.19184/IJC.2019.3.1.5","url":null,"abstract":"<p>An oriented <span class=\"math\"><em>k</em> − </span>coloring of an oriented graph <span class=\"math\"><em>G⃗</em></span> is a partition of <span class=\"math\"><em>V</em>(<em>G⃗</em>)</span> into <span class=\"math\"><em>k</em></span> color classes such that no two adjacent vertices belong to the same color class, and all the arcs linking the two color classes have the same direction. The oriented chromatic number of an oriented graph <span class=\"math\"><em>G⃗</em></span> is the minimum order of an oriented graph <span class=\"math\"><em>H⃗</em></span> to which <span class=\"math\"><em>G⃗</em></span> admits a homomorphism to <span class=\"math\"><em>H⃗</em></span>. The oriented chromatic number of an undirected graph <span class=\"math\"><em>G</em></span> is the maximum oriented chromatic number of all possible orientations of the graph <span class=\"math\"><em>G</em></span>. In this paper, we show that every edge amalgamation of cycle graphs, which also known as a book graph, has oriented chromatic number less than or equal to six.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83738325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on the metric dimension of subdivided thorn graphs","authors":"L. Yulianti, Narwen Narwen, Sri Hariyani","doi":"10.19184/IJC.2019.3.1.4","DOIUrl":"https://doi.org/10.19184/IJC.2019.3.1.4","url":null,"abstract":"<p>For some ordered subset <span class=\"math\"><em>W</em> = {<em>w</em>₁, <em>w</em>₂, ⋯, <em>w</em>_<em>t</em>}</span> of vertices in connected graph <span class=\"math\"><em>G</em></span>, and for some vertex <span class=\"math\"><em>v</em></span> in <span class=\"math\"><em>G</em></span>, the metric representation of <span class=\"math\"><em>v</em></span> with respect to <span class=\"math\"><em>W</em></span> is defined as the <span class=\"math\"><em>t</em></span>-vector <span class=\"math\"><em>r</em>(<em>v</em>∣<em>W</em>) = {<em>d</em>(<em>v</em>, <em>w</em>₁), <em>d</em>(<em>v</em>, <em>w</em>₂), ⋯, <em>d</em>(<em>v</em>, <em>w</em>_<em>t</em>)}</span>. The set <span class=\"math\"><em>W</em></span> is the resolving set of <span class=\"math\"><em>G</em></span> if for every two vertices <span class=\"math\"><em>u</em>, <em>v</em></span> in <span class=\"math\"><em>G</em></span>, <span class=\"math\"><em>r</em>(<em>u</em>∣<em>W</em>) ≠ <em>r</em>(<em>v</em>∣<em>W</em>)</span>. The metric dimension of <span class=\"math\"><em>G</em></span>, denoted by <span class=\"math\">dim(<em>G</em>)</span>, is defined as the minimum cardinality of <span class=\"math\"><em>W</em></span>. Let <span class=\"math\"><em>G</em></span> be a connected graph on <span class=\"math\"><em>n</em></span> vertices. The thorn graph of <span class=\"math\"><em>G</em></span>, denoted by <span class=\"math\"><em>T</em><em>h</em>(<em>G</em>, <em>l</em>₁, <em>l</em>₂, ⋯, <em>l</em>_<em>n</em>)</span>, is constructed from <span class=\"math\"><em>G</em></span> by adding <span class=\"math\"><em>l</em>_<em>i</em></span> leaves to vertex <span class=\"math\"><em>v</em>_<em>i</em></span> of <span class=\"math\"><em>G</em></span>, for <span class=\"math\"><em>l</em>_<em>i</em> ≥ 1</span> and <span class=\"math\">1 ≤ <em>i</em> ≤ <em>n</em></span>. The subdivided-thorn graph, denoted by <span class=\"math\"><em>T</em><em>D</em>(<em>G</em>, <em>l</em>₁(<em>y</em>₁), <em>l</em>₂(<em>y</em>₂), ⋯, <em>l</em>_<em>n</em>(<em>y</em>_<em>n</em>))</span>, is constructed by subdividing every <span class=\"math\"><em>l</em>_<em>i</em></span> leaves of the thorn graph of <span class=\"math\"><em>G</em></span> into a path on <span class=\"math\"><em>y</em>_<em>i</em></span> vertices. In this paper the metric dimension of thorn of complete graph, <span class=\"math\">dim(<em>T</em><em>h</em>(<em>K</em>_<em>n</em>, <em>l</em>₁, <em>l</em>₂, ⋯, <em>l</em>_<em>n</em>))</span>, <span class=\"math\"><em>l</em>_<em>i</em> ≥ 1</span> are determined, partially answering the problem proposed by Iswadi et al . This paper also gives some conjectures for the lower bound of <span class=\"math\">dim(<em>T</em><em>h</em>(<em>G</em>, <em>l</em>₁, <em>l</em>₂, ⋯, <em>l</em>_<em>n</em>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81563881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exclusive graphs: a new link among labelings","authors":"Rikio Ichishima, F. Muntaner-Batle, Akito Oshima","doi":"10.19184/IJC.2019.3.1.1","DOIUrl":"https://doi.org/10.19184/IJC.2019.3.1.1","url":null,"abstract":"In this paper, we define a strongly felicitous graph to be lower-exclusive, upper-exclusive and exclusive depending on different restrictions for the vertex labels. With these new concepts, we show that the union of finite collection of strongly felicitous graphs, a lower-exclusive one and an upper-exclusive one results in a strongly felicitous graph. We also introduce the concept of decompositional graphs. By means of this, we provide some results involving the cartesian products of exclusive graphs.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"237 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76122988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}