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The Multiplicative Zagreb Indices of Nanostructures and Chains 纳米结构和链的乘法萨格勒布指数
离散数学期刊(英文) Pub Date : 2016-03-31 DOI: 10.4236/OJDM.2016.62008
Wei Gao, M. Farahani, M. Kanna
{"title":"The Multiplicative Zagreb Indices of Nanostructures and Chains","authors":"Wei Gao, M. Farahani, M. Kanna","doi":"10.4236/OJDM.2016.62008","DOIUrl":"https://doi.org/10.4236/OJDM.2016.62008","url":null,"abstract":"In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube, nanostar and polyomino chain.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"82-88"},"PeriodicalIF":0.0,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626856","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
Non-backtracking random walks and a weighted Ihara's theorem 非回溯随机漫步和加权伊哈拉定理
离散数学期刊(英文) Pub Date : 2016-03-17 DOI: 10.4236/OJDM.2016.64018
Mark Kempton
{"title":"Non-backtracking random walks and a weighted Ihara's theorem","authors":"Mark Kempton","doi":"10.4236/OJDM.2016.64018","DOIUrl":"https://doi.org/10.4236/OJDM.2016.64018","url":null,"abstract":"We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-backtracking walk to the transition matrix for the usual random walk. This allows us to determine the spectrum of the transition probability matrix of a non-backtracking random walk in the case of regular graphs and biregular graphs. As a corollary, we obtain a result of Alon et al. in [1] that in most cases, a non-backtracking random walk on a regular graph has a faster mixing rate than the usual random walk. In addition, we obtain an analogous result for biregular graphs.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"531 1","pages":"207-226"},"PeriodicalIF":0.0,"publicationDate":"2016-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626510","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: 33
Solving the Maximum Matching Problem on Bipartite Star123-Free Graphs in Linear Time 线性时间下二部star123自由图的最大匹配问题求解
离散数学期刊(英文) Pub Date : 2016-01-26 DOI: 10.4236/OJDM.2016.61003
Ruzayn Quaddoura
{"title":"Solving the Maximum Matching Problem on Bipartite Star123-Free Graphs in Linear Time","authors":"Ruzayn Quaddoura","doi":"10.4236/OJDM.2016.61003","DOIUrl":"https://doi.org/10.4236/OJDM.2016.61003","url":null,"abstract":"The \u0000bipartite Star123-free \u0000graphs were introduced by V. Lozin in [1] to generalize some already known classes of \u0000bipartite graphs. In this paper, we extend to bipartite Star123-free graphs a linear time algorithm of J. L. \u0000Fouquet, V. Giakoumakis and J. M. Vanherpe for finding a maximum matching in \u0000bipartite Star123, P7-free graphs presented in [2]. Our algorithm is a solution of Lozin’s \u0000conjecture.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"41 1","pages":"13-24"},"PeriodicalIF":0.0,"publicationDate":"2016-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626541","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 Mutually Orthogonal Graph-Path Squares 关于相互正交的图路径平方
离散数学期刊(英文) Pub Date : 2016-01-01 DOI: 10.4236/OJDM.2016.61002
R. El-Shanawany
{"title":"On Mutually Orthogonal Graph-Path Squares","authors":"R. El-Shanawany","doi":"10.4236/OJDM.2016.61002","DOIUrl":"https://doi.org/10.4236/OJDM.2016.61002","url":null,"abstract":"A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"51 1","pages":"7-12"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626480","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
Paired, Total, and Connected Domination on the Queen’s Graph Revisited 对女王图上的配对、总和连接支配的重新审视
离散数学期刊(英文) Pub Date : 2016-01-01 DOI: 10.4236/OJDM.2016.61001
Paul A. Burchett
{"title":"Paired, Total, and Connected Domination on the Queen’s Graph Revisited","authors":"Paul A. Burchett","doi":"10.4236/OJDM.2016.61001","DOIUrl":"https://doi.org/10.4236/OJDM.2016.61001","url":null,"abstract":"The question associated with total domination on the queen’s graph has a long and rich history, first having been posed by Ahrens in 1910 [1]. The question is this: What is the minimum number of queens needed so that every square of an n × n board is attacked? Beginning in 2005 with Amirabadi, Burchett, and Hedetniemi [2] [3], work on this problem, and two other related problems, has seen progress. Bounds have been given for the values of all three domination parameters on the queen’s graph. In this paper, formations of queens are given that provide new bounds for the values of total, paired, and connected domination on the queen’s graph, denoted , , and respectively. For any n × n board size, the new bound of is arrived at, along with the separate bounds of , for with , and , for with .","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"1-6"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626471","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: 3
Rank Functions of Fuzzy Greedoids 模糊网格的秩函数
离散数学期刊(英文) Pub Date : 2015-08-12 DOI: 10.4236/OJDM.2015.54006
S. Tedford
{"title":"Rank Functions of Fuzzy Greedoids","authors":"S. Tedford","doi":"10.4236/OJDM.2015.54006","DOIUrl":"https://doi.org/10.4236/OJDM.2015.54006","url":null,"abstract":"Fuzzy greedoids were recently introduced as a fuzzy set generalization of (crisp) greedoids. We characterize fuzzy languages which define fuzzy greedoids, give necessary properties and sufficient properties of the fuzzy rank function of a fuzzy greedoid, give a characterization of the rank function for a weighted greedoid, and discuss the rank closure of a fuzzy greedoid.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"05 1","pages":"65-73"},"PeriodicalIF":0.0,"publicationDate":"2015-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626195","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
Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles 环的边顶点支配集与边顶点支配多项式
离散数学期刊(英文) Pub Date : 2015-08-12 DOI: 10.4236/OJDM.2015.54007
A. Vijayan, J. Beula
{"title":"Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles","authors":"A. Vijayan, J. Beula","doi":"10.4236/OJDM.2015.54007","DOIUrl":"https://doi.org/10.4236/OJDM.2015.54007","url":null,"abstract":"Let G = (V, E) be a simple graph. A set S E(G) is an edge-vertex \u0000dominating set of G (or simply an ev-dominating set), if for all vertices v V(G); there exists an \u0000edge eS such that e dominates v. Let denote the family of all ev-dominating sets of with cardinality i. Let . In this paper, we \u0000obtain a recursive formula for . Using this \u0000recursive formula, we construct the polynomial, , which we call edge-vertex domination polynomial of (or simply an ev-domination polynomial of ) and obtain some \u0000properties of this polynomial.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"05 1","pages":"74-87"},"PeriodicalIF":0.0,"publicationDate":"2015-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626397","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: 3
Domination Number of Square of Cartesian Products of Cycles 循环的笛卡尔积的平方的支配数
离散数学期刊(英文) Pub Date : 2015-08-12 DOI: 10.4236/OJDM.2015.54008
M. Alishahi, Sakineh Hoseini Shalmaee
{"title":"Domination Number of Square of Cartesian Products of Cycles","authors":"M. Alishahi, Sakineh Hoseini Shalmaee","doi":"10.4236/OJDM.2015.54008","DOIUrl":"https://doi.org/10.4236/OJDM.2015.54008","url":null,"abstract":"A set  is a dominating set of G if every vertex of  is adjacent to at least one vertex of S. The cardinality of the smallest \u0000dominating set of G is called the \u0000domination number of G. The square G2 of a graph G is obtained from G by adding new edges between every two vertices having distance 2 \u0000in G. In this paper we study the \u0000domination number of square of graphs, find a bound for domination number of \u0000square of Cartesian product of cycles, and find the exact value for some of \u0000them.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"05 1","pages":"88-94"},"PeriodicalIF":0.0,"publicationDate":"2015-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626410","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: 3
A Combinatorial Analysis of Tree-Like Sentences 树状句子的组合分析
离散数学期刊(英文) Pub Date : 2015-07-17 DOI: 10.4236/OJDM.2015.53004
G. Labelle, Louise Laforest
{"title":"A Combinatorial Analysis of Tree-Like Sentences","authors":"G. Labelle, Louise Laforest","doi":"10.4236/OJDM.2015.53004","DOIUrl":"https://doi.org/10.4236/OJDM.2015.53004","url":null,"abstract":"A sentence over a finite alphabet A, is a finite sequence of non-empty words over A. More generally, we define a graphical sentence over A by attaching a non-empty word over A to each arrow and each loop of a connected directed graph (digraph, for short). Each word is written according to the direction of its corresponding arrow or loop. Graphical sentences can be used to encode sets of sentences in a compact way: the readable sentences of a graphical sentence being the sentences corresponding to directed paths in the digraph. We apply combinatorial equations on enriched trees and rooted trees, in the context of combinatorial species and Polya theories, to analyze parameters in classes of tree-like sentences. These are graphical sentences constructed on tree-like digraphs.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"05 1","pages":"32-53"},"PeriodicalIF":0.0,"publicationDate":"2015-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626120","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 Signed Domination Number of the Cartesian Product of Two Directed Cycles 关于两个有向环笛卡尔积的符号支配数
离散数学期刊(英文) Pub Date : 2015-07-17 DOI: 10.4236/OJDM.2015.53005
Ramy S. Shaheen
{"title":"On the Signed Domination Number of the Cartesian Product of Two Directed Cycles","authors":"Ramy S. Shaheen","doi":"10.4236/OJDM.2015.53005","DOIUrl":"https://doi.org/10.4236/OJDM.2015.53005","url":null,"abstract":"Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function  is called a signed dominating function (SDF) if  for each vertex . The weight  of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m,  (mod 3) and bounds for otherwise.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"24 1","pages":"54-64"},"PeriodicalIF":0.0,"publicationDate":"2015-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70626183","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: 3
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