{"title":"Odd Harmonious Labeling of <em>P</em><sub>n</sub> ⊵ <em>C</em><sub>4 </sub>and <em>P</em><sub>n</sub> ⊵ <em>D</em><sub>2</sub>(<em>C</em><sub>4</sub>)","authors":"Sabrina Shena Sarasvati, Ikhsanul Halikin, Kristiana Wijaya","doi":"10.19184/ijc.2021.5.2.5","DOIUrl":"https://doi.org/10.19184/ijc.2021.5.2.5","url":null,"abstract":"A graph <em>G</em> with <em>q</em> edges is said to be odd harmonious if there exists an injection <em>f</em>:<em>V</em>(<em>G</em>) → ℤ<sub>2q</sub> so that the induced function <em>f</em>*:<em>E</em>(<em>G</em>)→ {1,3,...,2<em>q</em>-1} defined by <em>f</em>*(<em>uv</em>)=<em>f</em>(<em>u</em>)+<em>f</em>(<em>v</em>) is a bijection.<p>Here we show that graphs constructed by edge comb product of path <em>P</em><sub>n</sub> and cycle on four vertices <em>C</em><sub>4</sub> or shadow of cycle of order four <em>D</em><sub>2</sub>(<em>C</em><sub>4</sub>) are odd harmonious.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75694131","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":"All unicyclic graphs of order n with locating-chromatic number n-3","authors":"E. Baskoro, Arfin Arfin","doi":"10.19184/ijc.2021.5.2.3","DOIUrl":"https://doi.org/10.19184/ijc.2021.5.2.3","url":null,"abstract":"<p class=\"p1\">Characterizing all graphs having a certain locating-chromatic number is not an easy task. In this paper, we are going to pay attention on finding all unicyclic graphs of order <em>n</em> (⩾ 6) and having locating-chromatic number <em>n</em>-3.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73853647","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}
M. Togan, Aysun Yurttas Gunes, M. Demirci, I. N. Cangul
{"title":"Some degree-based topological indices of triphenylene polyester","authors":"M. Togan, Aysun Yurttas Gunes, M. Demirci, I. N. Cangul","doi":"10.19184/IJC.2021.5.1.4","DOIUrl":"https://doi.org/10.19184/IJC.2021.5.1.4","url":null,"abstract":"Molecules can be modelled by graphs to obtain their required properties by means of only mathematical methods and formulae. In this paper, several degree-based graph indices of one of the important chemical compounds called as polyester are calculated to determine several chemical and physicochemical properties of polyester.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86080889","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":"Broader families of cordial graphs","authors":"Christian Barrientos, S. Minion","doi":"10.19184/IJC.2021.5.1.6","DOIUrl":"https://doi.org/10.19184/IJC.2021.5.1.6","url":null,"abstract":"A binary labeling of the vertices of a graph G is cordial if the number of vertices labeled 0 and the number of vertices labeled 1 differ by at most 1, and the number of edges of weight 0 and the number of edges of weight 1 differ by at most 1. In this paper we present general results involving the cordiality of graphs that results of some well-known operations such as the join, the corona, the one-point union, the splitting graph, and the super subdivision. In addition we show a family of cordial circulant graphs.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80738091","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}
Khairannisa Al Azizu, L. Yulianti, Narwen Narwen, S. Sy
{"title":"On Super (a,d)-edge antimagic total labeling of branched-prism graph","authors":"Khairannisa Al Azizu, L. Yulianti, Narwen Narwen, S. Sy","doi":"10.19184/IJC.2021.5.1.2","DOIUrl":"https://doi.org/10.19184/IJC.2021.5.1.2","url":null,"abstract":"Let <em>H</em> be a branched-prism graph, denoted by <em>H</em> = (<em>C<sub>m</sub></em> x <em>P</em><sub>2</sub>) ⊙ Ǩ<sub>n</sub> for odd <em>m</em>, <em>m</em> ≥ 3 and <em>n</em> ≥ 1. This paper considers about the existence of the super (<em>a</em>,<em>d</em>)-edge antimagic total labeling of <em>H</em>, for some positive integer <em>a</em> and some non-negative integer <em>d</em>.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"165 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77484588","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":"Total edge irregularity strength of some cycle related graphs","authors":"Ramalakshmi Rajendran, K. Kathiresan","doi":"10.19184/IJC.2021.5.1.3","DOIUrl":"https://doi.org/10.19184/IJC.2021.5.1.3","url":null,"abstract":"<p>An edge irregular total <em>k</em>-labeling <em>f</em> : <em>V</em> ∪ <em>E</em> → 1,2, ..., <em>k</em> of a graph <em>G</em> = (<em>V,E</em>) is a labeling of vertices and edges of <em>G</em> in such a way that for any two different edges <em>uv</em> and <em>u'v'</em>, their weights <em>f</em>(<em>u</em>)+<em>f</em>(<em>uv</em>)+<em>f</em>(<em>v</em>) and <em>f</em>(<em>u'</em>)+<em>f</em>(<em>u'v'</em>)+<em>f</em>(<em>v'</em>) are distinct. The total edge irregularity strength tes(<em>G</em>) is defined as the minimum <em>k</em> for which the graph <em>G</em> has an edge irregular total <em>k</em>-labeling. In this paper, we determine the total edge irregularity strength of new classes of graphs <em>C<sub>m</sub></em> @ <em>C<sub>n</sub></em>, <em>P<sub>m,n</sub></em>* and <em>C<sub>m,n</sub></em>* and hence we extend the validity of the conjecture tes(<em>G</em>) = max {⌈|<em>E</em>(<em>G</em>)|+2)/3⌉, ⌈(Δ(<em>G</em>)+1)/2⌉}<em> </em> for some more graphs.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89344018","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":"Edge irregular reflexive labeling on sun graph and corona of cycle and null graph with two vertices","authors":"I. Setiawan, D. Indriati","doi":"10.19184/IJC.2021.5.1.5","DOIUrl":"https://doi.org/10.19184/IJC.2021.5.1.5","url":null,"abstract":"<p>Let <em>G</em>(<em>V</em>,<em>E</em>) be a simple and connected graph which set of vertices is <em>V</em> and set of edges is <em>E</em>. Irregular reflexive <em>k</em>-labeling f on <em>G</em>(<em>V</em>,<em>E</em>) is assignment that carries the numbers of integer to elements of graph, such that the positive integer {1,2, 3,...,<em>k</em><sub>e</sub>} assignment to edges of graph and the even positive integer {0,2,4,...,2<em>k</em><sub>v</sub>} assignment to vertices of graph. Then, we called as edge irregular reflexive <em>k</em>-labelling if every edges has different weight with <em>k</em> = max{<em>k</em><sub>e</sub>,2<em>k</em><sub>v</sub>}. Besides that, there is definition of reflexive edge strength of <em>G</em>(<em>V</em>,<em>E</em>) denoted as <em>res</em>(<em>G</em>), that is a minimum <em>k</em> that using for labeling <em>f</em> on <em>G</em>(<em>V</em>,<em>E</em>). This paper will discuss about edge irregular reflexive <em>k</em>-labeling for sun graph and corona of cycle and null graph, denoted by <em>C</em><sub>n</sub> ⨀ <em>N</em><sub>2</sub> and make sure about their reflexive edge strengths.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90160570","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":"Computing the split domination number of grid graphs","authors":"V. Girish, P. Usha","doi":"10.19184/IJC.2021.5.1.1","DOIUrl":"https://doi.org/10.19184/IJC.2021.5.1.1","url":null,"abstract":"<p>A set <em>D</em> - <em>V</em> is a dominating set of <em>G</em> if every vertex in <em>V - D</em> is adjacent to some vertex in <em>D</em>. The dominating number γ(<em>G</em>) of <em>G</em> is the minimum cardinality of a dominating set <em>D</em>. A dominating set <em>D</em> of a graph <em>G</em> = (<em>V;E</em>) is a split dominating set if the induced graph (<em>V</em> - <em>D</em>) is disconnected. The split domination number γ<em><sub>s</sub></em>(<em>G</em>) is the minimum cardinality of a split domination set. In this paper we have introduced a new method to obtain the split domination number of grid graphs by partitioning the vertex set in terms of star graphs and also we have<br />obtained the exact values of γ<em>s</em>(<em>G<sub>m;n</sub></em>); <em>m</em> ≤ <em>n</em>; <em>m,n</em> ≤ 24:</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"41 9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89244135","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 total disjoint irregularity strength of some certain graphs","authors":"M. Tilukay, A. Salman","doi":"10.19184/IJC.2020.4.2.2","DOIUrl":"https://doi.org/10.19184/IJC.2020.4.2.2","url":null,"abstract":"<div class=\"page\" title=\"Page 1\"><div class=\"layoutArea\"><div class=\"column\"><p><span>Under a totally irregular total </span><em>k</em><span>-labeling of a graph </span><span><em>G</em> </span><span>= (</span><span><em>V</em>,<em>E</em></span><span>), we found that for some certain graphs, the edge-weight set </span><em>W</em><span>(</span><em>E</em><span>) and the vertex-weight set </span><em>W</em><span>(</span><em>V</em><span>) of </span><span><em>G</em> </span><span>which are induced by </span><span><em>k</em> </span><span>= </span><span>ts</span><span>(</span><em>G</em><span>), </span><em>W</em><span>(</span><em>E</em><span>) </span><span>∩ </span><em>W</em><span>(</span><em>V</em><span>) is a non empty set. For which </span><span>k</span><span>, a graph </span><span>G </span><span>has a totally irregular total labeling if </span><em>W</em><span>(</span><em>E</em><span>) </span><span>∩ </span><em>W</em><span>(</span><em>V</em><span>) = </span><span>∅</span><span>? We introduce the total disjoint irregularity strength, denoted by </span><span>ds</span><span>(</span><em>G</em><span>), as the minimum value </span><span><em>k</em> </span><span>where this condition satisfied. We provide the lower bound of </span><span>ds</span><span>(</span><em>G</em><span>) and determine the total disjoint irregularity strength of cycles, paths, stars, and complete graphs.</span></p></div></div></div>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88756898","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 forcing monophonic and forcing geodetic numbers of a graph","authors":"J. John","doi":"10.19184/IJC.2020.4.2.5","DOIUrl":"https://doi.org/10.19184/IJC.2020.4.2.5","url":null,"abstract":"<p>For a connected graph <em>G</em> = (<em>V</em>, <em>E</em>), let a set <em>S</em> be a <em>m</em>-set of <em>G</em>. A subset <em>T</em> ⊆ <em>S</em> is called a forcing subset for <em>S</em> if <em>S</em> is the unique <em>m</em>-set containing <em>T</em>. A forcing subset for S of minimum cardinality is a minimum forcing subset of <em>S</em>. The forcing monophonic number of S, denoted by <em>fm</em>(<em>S</em>), is the cardinality of a minimum forcing subset of <em>S</em>. The forcing monophonic number of <em>G</em>, denoted by fm(G), is <em>fm</em>(<em>G</em>) = min{<em>fm</em>(<em>S</em>)}, where the minimum is taken over all minimum monophonic sets in G. We know that <em>m</em>(<em>G</em>) ≤ <em>g</em>(<em>G</em>), where <em>m</em>(<em>G</em>) and <em>g</em>(<em>G</em>) are monophonic number and geodetic number of a connected graph <em>G</em> respectively. However there is no relationship between <em>fm</em>(<em>G</em>) and <em>fg</em>(<em>G</em>), where <em>fg</em>(<em>G</em>) is the forcing geodetic number of a connected graph <em>G</em>. We give a series of realization results for various possibilities of these four parameters.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86380246","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}
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