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Indonesian Journal of Combinatorics最新文献

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On graphs with α- and b-edge consecutive edge magic labelings 关于具有α边和b边连续幻标记的图
Indonesian Journal of Combinatorics Pub Date : 2022-06-30 DOI: 10.19184/ijc.2022.6.1.4
Christian Barrientos
{"title":"On graphs with α- and b-edge consecutive edge magic labelings","authors":"Christian Barrientos","doi":"10.19184/ijc.2022.6.1.4","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.1.4","url":null,"abstract":"<p>Among the most studied graph labelings we have the varieties called alpha and edge-magic. Even when their definitions seem completely different, these labelings are related. A graceful labeling of a bipartite graph is called an α-labeling if the smaller labels are assigned to vertices of the same stable set. An edge-magic labeling of a graph of size <em>n</em> is said to be <em>b</em>-edge consecutive when its edges are labeled with the integers <em>b+1</em>, <em>b+2</em>, ..., <em>b+n</em>, for some 0 ≤ <em>b</em> ≤ <em>n</em>. In this work, we prove the existence of several <em>b</em> edge-magic labelings for any graph of order <em>m</em> and size <em>m-1</em> that admits an α-labeling. In addition, we determine the exact value of <em>b</em> induced by the α-labeling, as well as for its reverse, complementary, and reverse complementary labelings.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90978929","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}
引用次数: 0
Eigenvalues of antiadjacency matrix of Cayley graph of Z_n Z_n的Cayley图的反邻接矩阵特征值
Indonesian Journal of Combinatorics Pub Date : 2022-06-30 DOI: 10.19184/ijc.2022.6.1.5
J. Daniel., K. Sugeng, N. Hariadi
{"title":"Eigenvalues of antiadjacency matrix of Cayley graph of Z_n","authors":"J. Daniel., K. Sugeng, N. Hariadi","doi":"10.19184/ijc.2022.6.1.5","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.1.5","url":null,"abstract":"In this paper, we give a relation between the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) and the eigenvalues of the antiadjacency matrix of Cay(Z_n, (Z_n−{0})−S), as well as the eigenvalues of the adjacency matrix of Cay(Z_n, S). Then, we give the characterization of connection set S where the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) are all integers.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"563 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87021988","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}
引用次数: 0
The local metric dimension of split and unicyclic graphs 分裂图和单环图的局部度量维数
Indonesian Journal of Combinatorics Pub Date : 2022-06-28 DOI: 10.19184/ijc.2022.6.1.3
Dinny Fitriani, Anisa Rarasati, S. Saputro, E. Baskoro
{"title":"The local metric dimension of split and unicyclic graphs","authors":"Dinny Fitriani, Anisa Rarasati, S. Saputro, E. Baskoro","doi":"10.19184/ijc.2022.6.1.3","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.1.3","url":null,"abstract":"A set <em>W</em> is called a local resolving set of <em>G</em> if the distance of <em>u</em> and <em>v</em> to some elements of <em>W</em> are distinct for every two adjacent vertices <em>u</em> and <em>v</em> in <em>G</em>.  The local metric dimension of <em>G</em> is the minimum cardinality of a local resolving set of <em>G</em>.  A connected graph <em>G</em> is called a split graph if <em>V</em>(<em>G</em>) can be partitioned into two subsets <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> where an induced subgraph of G by <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> is a complete graph and an independent set, respectively.  We also consider a graph, namely the unicyclic graph which is a connected graph containing exactly one cycle.  In this paper, we provide a general sharp bounds of local metric dimension of split graph.  We also determine an exact value of local metric dimension of any unicyclic graphs.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86435601","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}
引用次数: 1
Prime ideal graphs of commutative rings 交换环的素数理想图
Indonesian Journal of Combinatorics Pub Date : 2022-06-27 DOI: 10.19184/ijc.2022.6.1.2
H. M. Salih, Asaad A. Jund
{"title":"Prime ideal graphs of commutative rings","authors":"H. M. Salih, Asaad A. Jund","doi":"10.19184/ijc.2022.6.1.2","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.1.2","url":null,"abstract":"Let R be a finite commutative ring with identity and P be a prime ideal of R. The vertex set is R - {0} and two distinct vertices are adjacent if their product in P. This graph is called the prime ideal graph of R and denoted by ΓP. The relationship among prime ideal, zero-divisor, nilpotent and unit graphs are studied. Also, we show that ΓP is simple connected graph with diameter less than or equal to two and both the clique number and the chromatic number of the graph are equal. Furthermore, it has girth 3 if it contains a cycle. In addition, we compute the number of edges of this graph and investigate some properties of ΓP.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"110 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87698901","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}
引用次数: 2
The complete short proof of the Berge conjecture 贝尔热猜想的完整简短证明
Indonesian Journal of Combinatorics Pub Date : 2022-06-27 DOI: 10.19184/ijc.2022.6.1.1
Ikorong Anouk
{"title":"The complete short proof of the Berge conjecture","authors":"Ikorong Anouk","doi":"10.19184/ijc.2022.6.1.1","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.1.1","url":null,"abstract":"<p>We say that a graph <em>B</em> is berge if every graph <em>B'</em> ∈ {<em>B</em>,<em>B̄</em><em></em>} does not contain an induced cycle of odd length ≥ 5 [<span><em>B̄</em></span> is the complementary graph of <em>B</em>}.</p><p>A graph G is perfect if every induced subgraph <em>G'</em> of <em>G</em> satisfies <em>χ</em>(<em>G'</em>)=<em>ω</em>(<em>G'</em>), where <em>χ</em>(<em>G'</em>) is the chromatic number of <em>G'</em> and <em>ω</em>(<em>G'</em>) is the clique number of <em>G'</em>. The Berge conjecture states that a graph <em>H</em> is perfect if and only if <em>H</em> is berge. Indeed, the Berge problem (or the difficult part of the Berge conjecture) consists to show that <em>χ</em>(<em>B</em>)=<em>ω</em>(<em>B</em>) for every berge graph <em>B</em>. In this paper, we give the direct short proof of the Berge conjecture by reducing the Berge problem into a simple equation of three unknowns and by using trivial complex calculus coupled with elementary computation and a trivial reformulation of that problem via the reasoning by reduction to absurd [we recall that the Berge conjecture was first proved by Chudnovsky, Robertson, Seymour and Thomas in a paper of at least 143 pages long. That being said, the new proof given in this paper is far more easy and more short].</p><p>Our work in this paper is original and is completely different from all strong investigations made by Chudnovsky, Robertson, Seymour and Thomas in their manuscript of at least 143 pages long.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82419366","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}
引用次数: 0
On local antimagic vertex coloring of corona products related to friendship and fan graph 关于友谊和扇子图的电晕积的局部反幻顶点着色
Indonesian Journal of Combinatorics Pub Date : 2021-12-28 DOI: 10.19184/ijc.2021.5.2.7
Zein Rasyid Himami, D. R. Silaban
{"title":"On local antimagic vertex coloring of corona products related to friendship and fan graph","authors":"Zein Rasyid Himami, D. R. Silaban","doi":"10.19184/ijc.2021.5.2.7","DOIUrl":"https://doi.org/10.19184/ijc.2021.5.2.7","url":null,"abstract":"Let <em>G</em>=(<em>V</em>,<em>E</em>) be connected graph. A bijection <em>f </em>: <em>E</em> → {1,2,3,..., |<em>E</em>|} is a local antimagic of <em>G</em> if any adjacent vertices <em>u,v</em> ∈ <em>V</em> satisfies <em>w</em>(<em>u</em>)≠ <em>w</em>(<em>v</em>), where <em>w</em>(<em>u</em>)=∑<sub>e∈E(u) </sub><em>f</em>(<em>e</em>), <em>E</em>(<em>u</em>) is the set of edges incident to <em>u</em>. When vertex <em>u</em> is assigned the color <em>w</em>(<em>u</em>), we called it a local antimagic vertex coloring of <em>G</em>. A local antimagic chromatic number of <em>G</em>, denoted by <em>χ</em><sub>la</sub>(<em>G</em>), is the minimum number of colors taken over all colorings induced by the local antimagic labeling of <em>G</em>. In this paper, we determine the local antimagic chromatic number of corona product of friendship and fan with null graph on <em>m</em> vertices, namely, <em>χ</em><sub>la</sub>(<em>F</em><sub>n</sub> ⊙ overline{K_m}) and <em>χ</em><sub>la</sub>(<em>f</em><sub>(1,n)</sub> ⊙ overline{K_m}).","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73530329","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}
引用次数: 1
The degree sequences of a graph with restrictions 带限制的图的度序列
Indonesian Journal of Combinatorics Pub Date : 2021-12-28 DOI: 10.19184/ijc.2021.5.2.2
Rikio Ichishima, F. Muntaner-Batle, M. Rius-Font, Yukio Takahashi
{"title":"The degree sequences of a graph with restrictions","authors":"Rikio Ichishima, F. Muntaner-Batle, M. Rius-Font, Yukio Takahashi","doi":"10.19184/ijc.2021.5.2.2","DOIUrl":"https://doi.org/10.19184/ijc.2021.5.2.2","url":null,"abstract":"<p>Two finite sequences <em>s</em><sub>1 </sub>and <em>s</em><sub>2</sub> of nonnegative integers are called bigraphical if there exists a bipartite graph <em>G</em> with partite sets <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> such that <em>s</em><sub>1</sub> and <em>s</em><sub>2</sub> are the degrees in <em>G </em>of the vertices in <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub>, respectively. In this paper, we introduce the concept of <em>1</em>-graphical sequences and present a necessary and sufficient condition for a sequence to be <em>1</em>-graphical in terms of bigraphical sequences.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83069207","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}
引用次数: 0
On the Locating Chromatic Number of Barbell Shadow Path Graph 关于杠铃阴影路径图色数的定位
Indonesian Journal of Combinatorics Pub Date : 2021-12-28 DOI: 10.19184/ijc.2021.5.2.4
A. Asmiati, Maharani Damayanti, L. Yulianti
{"title":"On the Locating Chromatic Number of Barbell Shadow Path Graph","authors":"A. Asmiati, Maharani Damayanti, L. Yulianti","doi":"10.19184/ijc.2021.5.2.4","DOIUrl":"https://doi.org/10.19184/ijc.2021.5.2.4","url":null,"abstract":"The locating-chromatic number was introduced by Chartrand in 2002. The locating chromatic number of a graph is a combined concept between the coloring and partition dimension of a graph. The locating chromatic number of a graph is defined as the cardinality of the minimum color classes of the graph. In this paper, we discuss about the locating-chromatic number of shadow path graph and barbell graph containing shadow graph.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"116 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86067781","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}
引用次数: 1
Relationship between adjacency and distance matrix of graph of diameter two 直径为2的图的邻接矩阵与距离矩阵的关系
Indonesian Journal of Combinatorics Pub Date : 2021-12-28 DOI: 10.19184/ijc.2021.5.2.1
S. L. Chasanah, Elvi Khairunnisa, Muhammad Yusuf, K. Sugeng
{"title":"Relationship between adjacency and distance matrix of graph of diameter two","authors":"S. L. Chasanah, Elvi Khairunnisa, Muhammad Yusuf, K. Sugeng","doi":"10.19184/ijc.2021.5.2.1","DOIUrl":"https://doi.org/10.19184/ijc.2021.5.2.1","url":null,"abstract":"The relationship among every pair of vertices in a graph can be represented as a matrix, such as in adjacency matrix and distance matrix. Both adjacency and distance matrices have the same property. Adjacency and distance matrices are both symmetric matrix with diagonals entries equals to 0.  In this paper, we discuss relationships between adjacency matrix and distance matrix of a graph of diameter two, which is D=2(J-I)-A. From this relationship, we  also determine the value of the determinant matrix A+D and the upper bound of determinant of matrix D.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73021000","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}
引用次数: 0
Structure of intersection graphs 交图的结构
Indonesian Journal of Combinatorics Pub Date : 2021-12-28 DOI: 10.19184/ijc.2021.5.2.6
H. M. Mohammed Salih, S. Omer
{"title":"Structure of intersection graphs","authors":"H. M. Mohammed Salih, S. Omer","doi":"10.19184/ijc.2021.5.2.6","DOIUrl":"https://doi.org/10.19184/ijc.2021.5.2.6","url":null,"abstract":"<p style=\"text-align: left;\" dir=\"ltr\"> Let <em>G</em> be a finite group and let <em>N</em> be a fixed normal subgroup of <em>G</em>.  In this paper, a new kind of graph on <em>G</em>, namely the intersection graph is defined and studied. We use <img src=\"/public/site/images/ikhsan/equation.png\" alt=\"\" width=\"6\" height=\"4\" /> to denote this graph, with its vertices are all normal subgroups of <em>G</em> and two distinct vertices are adjacent if their intersection in <em>N</em>. We show some properties of this graph. For instance, the intersection graph is a simple connected with diameter at most two. Furthermore we give the graph structure of <img src=\"/public/site/images/ikhsan/equation_(1).png\" alt=\"\" width=\"6\" height=\"4\" /> for some finite groups such as the symmetric, dihedral, special linear group, quaternion and cyclic groups. </p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87321495","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}
引用次数: 2
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