发布求助
文献互助 智能选刊 最新文献

Indonesian Journal of Combinatorics最新文献

筛选
英文 中文
On Ramsey (mK2,bPn)-minimal Graphs 关于拉姆齐（mK2,bPn）最小图
Indonesian Journal of Combinatorics Pub Date : 2023-07-05 DOI: 10.19184/ijc.2023.7.1.2
Nadia Nadia, L. Yulianti, F. F. Hadiputra
{"title":"On Ramsey (mK2,bPn)-minimal Graphs","authors":"Nadia Nadia, L. Yulianti, F. F. Hadiputra","doi":"10.19184/ijc.2023.7.1.2","DOIUrl":"https://doi.org/10.19184/ijc.2023.7.1.2","url":null,"abstract":"<p style=\"text-align: justify;\">Let <em>G</em> and <em>H</em> be two given graphs. The notation <em>F</em>→(<em>G,H</em>) means that any red-blue coloring on the edges of <em>F</em> will create either a red subgraph <em>G</em> or a blue subgraph <em>H</em> in <em>F</em>. A graph <em>F</em> is a Ramsey (<em>G,H</em>)-minimal graph if <em>F</em> satisfies two conditions: (1) <em>F→</em>(<em>G,H</em>), and (2) (<em>F</em>−<em>e</em>) ⇸ (<em>G,H</em>) for every <em>e </em>∈ <em>E</em>(<em>F</em>). Denote ℜ(<em>G,H</em>) as the set of all (<em>G,H</em>)-minimal graphs. In this paper we prove that a tree <em>T</em> is not in ℜ(<em>mK</em><sub>2</sub>,<em>bP</em><sub>n</sub>) if it has a diameter of at least <em>n</em>(<em>b+m</em>−1)−1 for <em>m,n,b</em>≥2, furthermore we show that (<em>b</em>+<em>m</em>−1)<em>P</em><sub>n</sub> ∈ ℜ(<em>mK</em><sub>2</sub>,<em>bP</em><sub>n</sub>) for every <em>m,n,b</em>≥2. We also prove that for <em>n</em>≥3, a cycle on <em>k</em> vertices is in ℜ(<em>mK</em><sub>2</sub>,<em>bP</em><sub>n</sub>) if and only if <em>k</em> ∈ [<em>n</em>(<em>b</em>+<em>m</em>−2)+1, <em>n</em>(<em>b</em>+<em>m</em>−1)−1].</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139362527","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
A note on vertex irregular total labeling of trees 关于树的顶点不规则总标注的说明
Indonesian Journal of Combinatorics Pub Date : 2023-07-05 DOI: 10.19184/ijc.2023.7.1.1
Faisal Susanto, R. Simanjuntak, E. Baskoro
{"title":"A note on vertex irregular total labeling of trees","authors":"Faisal Susanto, R. Simanjuntak, E. Baskoro","doi":"10.19184/ijc.2023.7.1.1","DOIUrl":"https://doi.org/10.19184/ijc.2023.7.1.1","url":null,"abstract":"The total vertex irregularity strength of a graph <em>G=</em>(<em>V,E</em>) is the minimum integer <em>k</em> so that there is a mapping from <em>V ∪ E</em> to the set {<em>1,2,...,k</em>} so that the vertex-weights (i.e., the sum of labels of a vertex together with the edges incident to it) are all distinct. In this note, we present a new sufficient condition for a tree to have total vertex irregularity strength ⌈(<em>n</em><sub>1</sub><em>+1</em>)<em>/2</em>⌉<em><em>, where <em>n<sub>1</sub></em> is the number of vertices of degree one in the tree.</em></em>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"97 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139362499","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
Γ-supermagic labeling of products of two cycles with cyclic groups 两个循环与循环基团的乘积的Γ-超神奇标记
Indonesian Journal of Combinatorics Pub Date : 2023-07-05 DOI: 10.19184/ijc.2023.7.1.3
D. Froncek
{"title":"Γ-supermagic labeling of products of two cycles with cyclic groups","authors":"D. Froncek","doi":"10.19184/ijc.2023.7.1.3","DOIUrl":"https://doi.org/10.19184/ijc.2023.7.1.3","url":null,"abstract":"A <em>Γ</em>-supermagic labeling of a graph <em>G</em>=(<em>V,E</em>) is a bijection from <em>E</em> to a group <em>Γ</em> of order |<em>E</em>| such that the sum of labels of all edges incident with any vertex <em>x</em>∈ <em>V</em> is equal to the same element μ ∈ <em>Γ</em>. <br /><br />A <em>Z</em><sub>2mn</sub>-supermagic labeling of the Cartesian product of two cycles, <em>C</em><sub>m</sub> ℺ <em>C</em><sub>n</sub> for every <em>m,n</em> ≥ 3 was found by Froncek, McKeown, McKeown, and McKeown. In this paper we present a <em>Z</em><sub>k</sub>-supermagic labeling of the direct and strong product by cyclic group <em>Z</em><sub>k</sub> for any <em>m,n</em> ≥ 3.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139362749","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
Local Strong Rainbow Connection Number of Corona Product Between Cycle Graphs 循环图之间日冕积的局部强彩虹连接数
Indonesian Journal of Combinatorics Pub Date : 2023-07-05 DOI: 10.19184/ijc.2023.7.1.4
Khairunnisa N. Afifah, Kiki A. Sugeng
{"title":"Local Strong Rainbow Connection Number of Corona Product Between Cycle Graphs","authors":"Khairunnisa N. Afifah, Kiki A. Sugeng","doi":"10.19184/ijc.2023.7.1.4","DOIUrl":"https://doi.org/10.19184/ijc.2023.7.1.4","url":null,"abstract":"<p style=\"text-align: justify;\">A rainbow geodesic is a shortest path between two vertices where all edges are colored differently. An edge coloring in which any pair of vertices with distance up to <em>d</em>, where <em>d</em> is a positive integer that can be connected by a rainbow geodesic is called <em>d</em>-local strong rainbow coloring. The <em>d</em>-local strong rainbow connection number, denoted by <em>lsrc</em><sub>d</sub>(<em>G</em>), is the least number of colors used in <em>d</em>-local strong rainbow coloring. Suppose that <em>G</em> and <em>H</em> are graphs of order <em>m</em> and <em>n</em>, respectively. The corona product of <em>G</em> and <em>H</em>, <em>G </em>⊙ <em>H</em>, is defined as a graph obtained by taking a copy of <em>G</em> and <em>m</em> copies of <em>H</em>, then connecting every vertex in the <em>i</em>-th copy of <em>H</em> to the <em>i</em>-th vertex of <em>G</em>. In this paper, we will determine the <em>lsrc</em><sub>d</sub>(<em>C</em><sub>m</sub> ⊙ <em>C</em><sub>n</sub>) for <em>d</em>=2 and <em>d</em>=3.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139362557","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 graphs associated to topological spaces 在与拓扑空间相关的图上
Indonesian Journal of Combinatorics Pub Date : 2023-06-30 DOI: 10.19184/ijc.2023.7.1.5
Haval Mohammed Salih
{"title":"On graphs associated to topological spaces","authors":"Haval Mohammed Salih","doi":"10.19184/ijc.2023.7.1.5","DOIUrl":"https://doi.org/10.19184/ijc.2023.7.1.5","url":null,"abstract":"Let 𝑋 be a set and (𝑋,𝑇) be a topological space. A new type of graph on 𝑃(𝑋), namely the closure graph of 𝑇 is introduced. The closure graph denoted by <em>Γ<sup>c</sup></em> whose vertex set is 𝑃(𝑋) in which two distinct vertices 𝐴 and 𝐵 are adjacent if <em>A</em>'∩<em>B</em>' ⊆ (<em>A</em>∩<em>B</em>)'. In this paper, the closure graph is shown as a simple, connected graph with diameter at most two. Furthermore, the girth of the closure graph <em>Γ<sup>c</sup></em>of 𝑇 is three if 𝑋 contains more than one point. Also, several graph properties are studied.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136369565","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 number of caterpillars 毛毛虫的数量
Indonesian Journal of Combinatorics Pub Date : 2022-12-31 DOI: 10.19184/ijc.2022.6.2.1
Christian Barrientos
{"title":"On the number of caterpillars","authors":"Christian Barrientos","doi":"10.19184/ijc.2022.6.2.1","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.2.1","url":null,"abstract":"<p style=\"text-align: justify;\">A caterpillar is a tree obtained from a path by attaching pendant vertices. The number of caterpillars of size <em>n</em> is a well-known result. In this work extend this result exploring the number of caterpillars of size <em>n</em> together with the cardinalities of the stable sets and the diameter. Three closed formulas are presented, giving the number of caterpillars of size <em>n</em> with: (i) smaller stable set of cardinality <em>k</em>, (ii) diameter <em>d</em>, and (iii) diameter <em>d</em> and smaller stable set of cardinality <em>k</em>.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81022466","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
Index graphs of finite permutation groups 有限置换群的索引图
Indonesian Journal of Combinatorics Pub Date : 2022-12-31 DOI: 10.19184/ijc.2022.6.2.2
H. M. Mohammed Salih
{"title":"Index graphs of finite permutation groups","authors":"H. M. Mohammed Salih","doi":"10.19184/ijc.2022.6.2.2","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.2.2","url":null,"abstract":"Let <em>G</em> be a subgroup of <em>S</em><sub>n</sub>. For <em>x ∈ G</em>, the index of <em>x</em> in <em>G</em> is denoted by <em>ind x</em> is the minimal number of 2-cycles needed to express <em>x</em> as a product. In this paper, we define a new kind of graph on <em>G</em>, namely the index graph and denoted by <em>Γ</em><sup>ind</sup><em>(G)</em>. Its vertex set the set of all conjugacy classes of <em>G</em> and two distinct vertices <em>x ∈ C</em><sub>x</sub> and <em>y ∈ C</em><sub>y</sub> are adjacent if <em>Gcd(ind x, ind y) 6 ≠ 1</em>. We study some properties of this graph for the symmetric groups <em>S</em><sub>n</sub>, the alternating group <em>A</em><sub>n</sub>, the cyclic group <em>C</em><sub>n</sub>, the dihedral group <em>D</em><sub>2n</sub> and the generalized quaternain group <em>Q</em><sub>4n</sub>. In particular, we are interested in the connectedness of them.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"2016 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86623175","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
Hamming index of graphs with respect to its incidence matrix 图相对于关联矩阵的汉明指数
Indonesian Journal of Combinatorics Pub Date : 2022-12-31 DOI: 10.19184/ijc.2022.6.2.4
H. Ramane, Ishwar Baidari, R. Jummannaver, V. V. Manjalapur, G. A. Gudodagi, A. Yalnaik, Ajith Hanagawadimath
{"title":"Hamming index of graphs with respect to its incidence matrix","authors":"H. Ramane, Ishwar Baidari, R. Jummannaver, V. V. Manjalapur, G. A. Gudodagi, A. Yalnaik, Ajith Hanagawadimath","doi":"10.19184/ijc.2022.6.2.4","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.2.4","url":null,"abstract":"Let $B(G)$ be the incidence matrix of a graph $G$. The row in $B(G)$ corresponding to a vertex $v$, denoted by $s(v)$ is the string which belongs to $Bbb{Z}_2^n$, a set of $n$-tuples over a field of order two. The Hamming distance between the strings $s(u)$ and $s(v)$ is the number of positions in which $s(u)$ and $s(v)$ differ. In this paper we obtain the Hamming distance between the strings generated by the incidence matrix of a graph. The sum of Hamming distances between all pairs of strings, called Hamming index of a graph is obtained.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87330361","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 total vertex irregularity strength of symmetric cubic graphs of the Foster's Census 福斯特普查中对称三次图的顶点总不规则强度
Indonesian Journal of Combinatorics Pub Date : 2022-12-31 DOI: 10.19184/ijc.2022.6.2.3
Rika Yanti, Gregory Benedict Tanidi, S. Saputro, E. Baskoro
{"title":"The total vertex irregularity strength of symmetric cubic graphs of the Foster's Census","authors":"Rika Yanti, Gregory Benedict Tanidi, S. Saputro, E. Baskoro","doi":"10.19184/ijc.2022.6.2.3","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.2.3","url":null,"abstract":"Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order n with n ≤ 512. This census then was continued by Conder et al. (2006) and they obtained the complete list of all connected symmetric cubic graphs with order n ≤ 768. In this paper, we determine the total vertex irregularity strength of such graphs obtained by Foster. As a result, all the values of the total vertex irregularity strengths of the symmetric cubic graphs of order n from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos & Salman (2010), namely ⌈(n+3)/4⌉.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74017498","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
On generalized composed properties of generalized product graphs 关于广义积图的广义组合性质
Indonesian Journal of Combinatorics Pub Date : 2022-12-31 DOI: 10.19184/ijc.2022.6.2.5
Nopparat Pleanmani, S. Panma
{"title":"On generalized composed properties of generalized product graphs","authors":"Nopparat Pleanmani, S. Panma","doi":"10.19184/ijc.2022.6.2.5","DOIUrl":"https://doi.org/10.19184/ijc.2022.6.2.5","url":null,"abstract":"<p>A property ℘ is defined to be a nonempty isomorphism-closed subclass of the class of all finite simple graphs. A nonempty set <em>S</em> of vertices of a graph <em>G</em> is said to be a ℘-set of <em>G</em> if <em>G</em>[<em>S</em>]∈ ℘. The maximum and minimum cardinalities of a ℘-set of <em>G</em> are denoted by <em>M</em><sub>℘</sub>(<em>G</em>) and <em>m</em><sub>℘</sub>(<em>G</em>), respectively. If <em>S</em> is a ℘-set such that its cardinality equals <em>M</em><sub>℘</sub>(<em>G</em>) or <em>m</em><sub>℘</sub>(<em>G</em>), we say that <em>S</em> is an <em>M</em><sub>℘</sub>-set or an <em>m</em><sub>℘</sub>-set of <em>G</em>, respectively. In this paper, we not only define six types of property ℘ by the using concepts of graph product and generalized graph product, but we also obtain <em>M</em><sub>℘</sub> and <em>m</em><sub>℘</sub> of product graphs in each type and characterize its <em>M</em><sub>℘</sub>-set.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87973685","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
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信