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{Ck, Pk, Sk} -Decompositions of Balanced Complete Bipartite Multigraphs {Ck, Pk, Sk} -平衡完全二部多图的分解
离散数学期刊(英文) Pub Date : 2016-06-21 DOI: 10.4236/OJDM.2016.63015
Jenq-Jong Lin, Min-Jen Jou
{"title":"{Ck, Pk, Sk} -Decompositions of Balanced Complete Bipartite Multigraphs","authors":"Jenq-Jong Lin, Min-Jen Jou","doi":"10.4236/OJDM.2016.63015","DOIUrl":"https://doi.org/10.4236/OJDM.2016.63015","url":null,"abstract":"Let be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer copies of Hi, where . Let Ck, Pk and Sk denote a cycle, a path and a star with k edges, respectively. For an integer , we prove that a balanced complete bipartite multigraph  has a -decomposition if and only if k is even, and .","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"174-179"},"PeriodicalIF":0.0,"publicationDate":"2016-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626842","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 Independence-Separation Problem on the 3-D Rook’s Graph 三维车图上的独立-分离问题
离散数学期刊(英文) Pub Date : 2016-06-21 DOI: 10.4236/OJDM.2016.63014
Paul A. Burchett
{"title":"The Independence-Separation Problem on the 3-D Rook’s Graph","authors":"Paul A. Burchett","doi":"10.4236/OJDM.2016.63014","DOIUrl":"https://doi.org/10.4236/OJDM.2016.63014","url":null,"abstract":"Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"167-173"},"PeriodicalIF":0.0,"publicationDate":"2016-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626796","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
Note on Cyclically Interval Edge Colorings of Simple Cycles 关于简单环的循环区间边着色的注记
离散数学期刊(英文) Pub Date : 2016-06-21 DOI: 10.4236/OJDM.2016.63016
Nannan Wang, Yongqiang Zhao
{"title":"Note on Cyclically Interval Edge Colorings of Simple Cycles","authors":"Nannan Wang, Yongqiang Zhao","doi":"10.4236/OJDM.2016.63016","DOIUrl":"https://doi.org/10.4236/OJDM.2016.63016","url":null,"abstract":"A proper edge t-coloring of a graph G is a coloring of its edges with colors  1, 2,..., t, such that all colors are used, and no two adjacent edges receive the same color. A cyclically interval t-coloring of a graph G is a proper edge t-coloring of G such that for each vertex, either the set of colors used on edges incident to x or the set of colors not used on edges incident to x forms an interval of integers. In this paper, we provide a new proof of the result on the colors in cyclically interval edge colorings of simple cycles which was first proved by Rafayel R. Kamalian in the paper “On a Number of Colors in Cyclically Interval Edge Colorings of Simple Cycles, Open Journal of Discrete Mathematics, 2013, 43-48”.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"180-184"},"PeriodicalIF":0.0,"publicationDate":"2016-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626441","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 ErdÖs Distance Conjecture in Geometry 论几何中的ErdÖs距离猜想
离散数学期刊(英文) Pub Date : 2016-06-21 DOI: 10.4236/OJDM.2016.63012
A. Jafari, Amin Najafi Amin
{"title":"On the ErdÖs Distance Conjecture in Geometry","authors":"A. Jafari, Amin Najafi Amin","doi":"10.4236/OJDM.2016.63012","DOIUrl":"https://doi.org/10.4236/OJDM.2016.63012","url":null,"abstract":"ErdOs asks if it is possible to have n points in general position in the plane (no three on a line or four on a circle) such that for every i (1≤i≤n-1 ) there is a distance determined by the points that occur exactly i times. So far some examples have been discovered for 2≤n≤8 [1] [2]. A solution for the 8 point is provided by I. Palasti [3]. Here two other possible solutions for the 8 point case as well as all possible answers to 4 - 7 point cases are provided and finally a brief discussion on the generalization of the problem to higher dimensions is given.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"109-160"},"PeriodicalIF":0.0,"publicationDate":"2016-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626817","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
Computation of Topological Indices of Dutch Windmill Graph 荷兰风车图拓扑指数的计算
离散数学期刊(英文) Pub Date : 2016-03-31 DOI: 10.4236/OJDM.2016.62007
M. Kanna, R. P. Kumar, R. Jagadeesh
{"title":"Computation of Topological Indices of Dutch Windmill Graph","authors":"M. Kanna, R. P. Kumar, R. Jagadeesh","doi":"10.4236/OJDM.2016.62007","DOIUrl":"https://doi.org/10.4236/OJDM.2016.62007","url":null,"abstract":"In this paper, we compute Atom-bond connectivity index, Fourth atom-bond connectivity index, Sum connectivity index, Randic connectivity index, Geometric-arithmetic connectivity index and Fifth geometric-arithmetic connectivity index of Dutch windmill graph.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"74-81"},"PeriodicalIF":0.0,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626736","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: 12
Algebra and Geometry of Sets in Boolean Space 布尔空间中集合的代数和几何
离散数学期刊(英文) Pub Date : 2016-03-31 DOI: 10.4236/OJDM.2016.62004
V. Leontiev, G. Movsisyan, Z. Margaryan
{"title":"Algebra and Geometry of Sets in Boolean Space","authors":"V. Leontiev, G. Movsisyan, Z. Margaryan","doi":"10.4236/OJDM.2016.62004","DOIUrl":"https://doi.org/10.4236/OJDM.2016.62004","url":null,"abstract":"In the \u0000present paper, geometry of the Boolean space Bn in terms of Hausdorff distances between subsets and \u0000subset sums is investigated. The main results are the algebraic and analytical \u0000expressions for representing of classical figures in Bn and the functions of distances between them. In \u0000particular, equations in sets are considered and their interpretations in \u0000combinatory terms are given.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"25-40"},"PeriodicalIF":0.0,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626667","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: 4
On Polynomials Rn(x) Related to the Stirling Numbers and the Bell Polynomials Associated with the p-Adic Integral on 关于Stirling数的多项式Rn(x)和关于p进积分的Bell多项式
离散数学期刊(英文) Pub Date : 2016-03-31 DOI: 10.4236/OJDM.2016.62009
H. Y. Lee, C. Ryoo
{"title":"On Polynomials Rn(x) Related to the Stirling Numbers and the Bell Polynomials Associated with the p-Adic Integral on","authors":"H. Y. Lee, C. Ryoo","doi":"10.4236/OJDM.2016.62009","DOIUrl":"https://doi.org/10.4236/OJDM.2016.62009","url":null,"abstract":"In this paper, one introduces the polynomials Rn(x) and numbers Rn and derives some interesting identities related to the numbers and polynomials: Rn and Rn(x). We also give relation between the Stirling numbers, the Bell numbers, the Rn and Rn(x).","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"89-98"},"PeriodicalIF":0.0,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626865","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 Rupture Degree of Graphs with k-Tree 具有k-树的图的破裂度
离散数学期刊(英文) Pub Date : 2016-03-31 DOI: 10.4236/OJDM.2016.62011
Yinkui Li, Qingning Wang, Xiaolin Wang
{"title":"The Rupture Degree of Graphs with k-Tree","authors":"Yinkui Li, Qingning Wang, Xiaolin Wang","doi":"10.4236/OJDM.2016.62011","DOIUrl":"https://doi.org/10.4236/OJDM.2016.62011","url":null,"abstract":"A k-tree of a connected graph G is a spanning tree with maximum degree \u0000at most k. The rupture degree for a \u0000connected graph G is defined by , where and , \u0000respectively, denote the order of the largest component and number of \u0000components in . In this \u0000paper, we show that for a connected graph G, \u0000if  for any cut-set , then G has a k-tree.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"105-107"},"PeriodicalIF":0.0,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626808","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 Maximum Number of Dominating Classes in Graph Coloring 论图着色中支配类的最大数目
离散数学期刊(英文) Pub Date : 2016-03-31 DOI: 10.4236/OJDM.2016.62006
B. Zhou
{"title":"On the Maximum Number of Dominating Classes in Graph Coloring","authors":"B. Zhou","doi":"10.4236/OJDM.2016.62006","DOIUrl":"https://doi.org/10.4236/OJDM.2016.62006","url":null,"abstract":"We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"70-73"},"PeriodicalIF":0.0,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626722","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: 8
Double Derangement Permutations 双错乱排列
离散数学期刊(英文) Pub Date : 2016-03-31 DOI: 10.4236/OJDM.2016.62010
Pooya Daneshmand, Kamyar Mirzavaziri, M. Mirzavaziri
{"title":"Double Derangement Permutations","authors":"Pooya Daneshmand, Kamyar Mirzavaziri, M. Mirzavaziri","doi":"10.4236/OJDM.2016.62010","DOIUrl":"https://doi.org/10.4236/OJDM.2016.62010","url":null,"abstract":"Let n be a positive integer. A permutation a of the symmetric group  of permutations of  is called a derangement if   for each . Suppose that x and y are two arbitrary permutations of . We say that a \u0000permutation a is a double \u0000derangement with respect to x and y if  and  for each . In this paper, we give an explicit formula for , the number of double \u0000derangements with respect to x and y. \u0000Let  and let  and  be two subsets of  with  and . Suppose that  denotes the number of derangements x such that . As the main result, \u0000we show that if  and z is a permutation such that  for  and  for , then  where .","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"99-104"},"PeriodicalIF":0.0,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626765","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
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