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The Generalization of Signed Domination Number of Two Classes of Graphs 两类图的有符号支配数的推广
离散数学期刊(英文) Pub Date : 2021-01-01 DOI: 10.4236/ojdm.2021.114009
Xia Hong, Guoyan Ao, F. Gao
{"title":"The Generalization of Signed Domination Number of Two Classes of Graphs","authors":"Xia Hong, Guoyan Ao, F. Gao","doi":"10.4236/ojdm.2021.114009","DOIUrl":"https://doi.org/10.4236/ojdm.2021.114009","url":null,"abstract":"","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70627158","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
Rational Points on Genus 3 Real Hyperelliptic Curves 属3实超椭圆曲线上的有理点
离散数学期刊(英文) Pub Date : 2021-01-01 DOI: 10.4236/ojdm.2021.114008
Brice M. Miayoka, R. F. Babindamana, B. G. R. Bossoto
{"title":"Rational Points on Genus 3 Real Hyperelliptic Curves","authors":"Brice M. Miayoka, R. F. Babindamana, B. G. R. Bossoto","doi":"10.4236/ojdm.2021.114008","DOIUrl":"https://doi.org/10.4236/ojdm.2021.114008","url":null,"abstract":"","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70627124","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 Signed Domination of Grid Graph 关于网格图的签名支配
离散数学期刊(英文) Pub Date : 2020-09-16 DOI: 10.4236/ojdm.2020.104010
M. Hassan, Muhsin Al Hassan, Mazen Mostafa
{"title":"On Signed Domination of Grid Graph","authors":"M. Hassan, Muhsin Al Hassan, Mazen Mostafa","doi":"10.4236/ojdm.2020.104010","DOIUrl":"https://doi.org/10.4236/ojdm.2020.104010","url":null,"abstract":"Let G(V, E) be a finite connected simple graph with vertex set V(G). A function is a signed dominating function f : V(G)→{−1,1} if for every vertex v ∈ V(G), the sum of closed neighborhood weights of v is greater or equal to 1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate the signed domination numbers of the Cartesian product of two paths Pm and Pn for m = 6, 7 and arbitrary n.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47090494","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
Full-Rank Factoring of Elementary 2-Groups with Equal Size Factors 因子大小相等的初等2群的全秩分解
离散数学期刊(英文) Pub Date : 2020-09-16 DOI: 10.4236/OJDM.2020.104009
Pécs, Hungary
{"title":"Full-Rank Factoring of Elementary 2-Groups with Equal Size Factors","authors":"Pécs, Hungary","doi":"10.4236/OJDM.2020.104009","DOIUrl":"https://doi.org/10.4236/OJDM.2020.104009","url":null,"abstract":"In order to answer a question motivated by constructing substitution boxes in block ciphers we will exhibit an infinite family of full-rank factorizations of elementary 2-groups into two factors having equal sizes.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"10 1","pages":"89-95"},"PeriodicalIF":0.0,"publicationDate":"2020-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41449271","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
Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup 利用非满射内射映射对任意无限集的划分及一个显著半群的研究
离散数学期刊(英文) Pub Date : 2020-06-15 DOI: 10.4236/ojdm.2020.103008
Charif Harrafa
{"title":"Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup","authors":"Charif Harrafa","doi":"10.4236/ojdm.2020.103008","DOIUrl":"https://doi.org/10.4236/ojdm.2020.103008","url":null,"abstract":"In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of non-surjective injective maps. The non-surjective injective maps from an infinite set to itself constitute a semigroup for the law of composition bundled with certain properties allowing us to prove the existence of remarkable elements. Not to mention a compatible equivalence relation that allows transferring the said law to the quotient set, which can be provided with a lattice structure. Finally, we will present the concept of Co-injectivity and some of its properties.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45155553","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 Signed Domination Number of Cartesian Product of Two Paths 两条路径的笛卡尔乘积的符号支配数
离散数学期刊(英文) Pub Date : 2020-01-22 DOI: 10.4236/ojdm.2020.102005
M. Hassan, Muhsin Al Hassan, Mazen Mostafa
{"title":"The Signed Domination Number of Cartesian Product of Two Paths","authors":"M. Hassan, Muhsin Al Hassan, Mazen Mostafa","doi":"10.4236/ojdm.2020.102005","DOIUrl":"https://doi.org/10.4236/ojdm.2020.102005","url":null,"abstract":"Let G be a finite connected simple graph with vertex set V(G) and edge set E(G). A function f:V(G) → {1,1} is a signed dominating function if for every vertex v∈V(G), the closed neighborhood of v contains more vertices with function values 1 than with −1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate The signed domination numbers of the Cartesian product of two paths Pm and Pn for m = 3, 4, 5 and arbitrary n.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43604913","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
Unique Efficient Dominating Sets 唯一有效支配集
离散数学期刊(英文) Pub Date : 2020-01-22 DOI: 10.4236/ojdm.2020.102006
Isaac Reiter, Ju Zhou
{"title":"Unique Efficient Dominating Sets","authors":"Isaac Reiter, Ju Zhou","doi":"10.4236/ojdm.2020.102006","DOIUrl":"https://doi.org/10.4236/ojdm.2020.102006","url":null,"abstract":"Given a finite simple graph G, a set D ⊆ V(G) is called a dominating set if for all v ∈ V(G) , either v ∈ D or v is adjacent to some vertex in D. A dominating set D is independent if none of the vertices in D are adjacent, and D is perfect if each vertex not in D is adjacent to precisely one vertex in D. If a dominating set is both independent and perfect, then it is called an efficient dominating set. For a graph G, a set D is called a unique efficient dominating set of G if it is the only efficient dominating set of G. In this paper, the authors propose the definition of unique efficient dominating set, explore the properties of graphs with unique efficient dominating sets, and completely characterize several families of graphs which have unique efficient dominating sets.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44733853","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 Number of Minimum Roman and Minimum Total Dominating Sets for Some Chessboard Graphs 若干棋盘图的最小罗马支配集和最小总支配集的数目
离散数学期刊(英文) Pub Date : 2020-01-16 DOI: 10.4236/ojdm.2020.101004
Paul A. Burchett
{"title":"The Number of Minimum Roman and Minimum Total Dominating Sets for Some Chessboard Graphs","authors":"Paul A. Burchett","doi":"10.4236/ojdm.2020.101004","DOIUrl":"https://doi.org/10.4236/ojdm.2020.101004","url":null,"abstract":"In this paper, both the roman domination number and the number of minimum roman dominating sets are found for any rectangular rook’s graph. In a similar fashion, the roman domination number and the number of minimum roman dominating sets are found on the square bishop’s graph for odd board sizes. Also found are the number of minimum total dominating sets associated with the light-colored squares when n ≡ 1(mod12)  (with n>1), and same for the dark-colored squares when n ≡ 7(mod12) .","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45256526","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
Infinite Sets of Related b-wARH Pairs 相关b-wARH对的无限集
离散数学期刊(英文) Pub Date : 2020-01-01 DOI: 10.4236/ojdm.2020.101001
Catalin Nitica, V. Nitica
{"title":"Infinite Sets of Related b-wARH Pairs","authors":"Catalin Nitica, V. Nitica","doi":"10.4236/ojdm.2020.101001","DOIUrl":"https://doi.org/10.4236/ojdm.2020.101001","url":null,"abstract":"Let b ≥ 2 be a numeration base. A b-weak additive Ramanujan-Hardy (or b-wARH) number N is a non-negative integer for which there exists at least one non-negative integer A, such that the sum of A and the sum of base b digits of N, added to the reversal of the sum, give N. We say that a pair of such numbers are related of degrees d ≥ 0 if their difference is d. We show for all numeration bases an infinity of degrees d for which there exists an infinity of pairs of b-wARH numbers related of degree d.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626916","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
Some Results on Cordial Digraphs 关于诚恳有向图的一些结果
离散数学期刊(英文) Pub Date : 2020-01-01 DOI: 10.4236/ojdm.2020.101002
M. M. Al-Shamiri, S. Nada, A. Elrokh, Yasser Elmshtaye
{"title":"Some Results on Cordial Digraphs","authors":"M. M. Al-Shamiri, S. Nada, A. Elrokh, Yasser Elmshtaye","doi":"10.4236/ojdm.2020.101002","DOIUrl":"https://doi.org/10.4236/ojdm.2020.101002","url":null,"abstract":"A digraph is a graph in which each edge has an orientation. A linear directed path, , is a path whose all edges have the same orientation. A linear simple graph is called directed cordial if it admits 0 - 1 labeling that satisfies certain condition. In this paper, we study the cordiality of directed paths  and their second power . Similar studies are done for  and the join  . We show that ,  and  are directed cordial. Sufficient conditions are given to the join   to be directed cordial.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"10 1","pages":"4-12"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626931","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: 6
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