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Transactions on Combinatorics最新文献

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The log-convexity of the fubini numbers 傅比尼数的对数凸性
IF 0.4
Transactions on Combinatorics Pub Date : 2018-06-01 DOI: 10.22108/TOC.2017.104212.1496
Qing Zou
{"title":"The log-convexity of the fubini numbers","authors":"Qing Zou","doi":"10.22108/TOC.2017.104212.1496","DOIUrl":"https://doi.org/10.22108/TOC.2017.104212.1496","url":null,"abstract":"Let $f_n$ denotes the $n$th Fubini number. In this paper, first we give upper and lower bounds for the Fubini numbers $f_n$. Then the log-convexity of the Fubini numbers has been obtained. Furthermore we also give the monotonicity of the sequence ${sqrt[n]{f_n}}_{nge 1}$ by using the aforementioned bounds.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"17-23"},"PeriodicalIF":0.4,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46650263","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
Combinatorial parameters on bargraphs of permutations 排列柱状图上的组合参数
IF 0.4
Transactions on Combinatorics Pub Date : 2018-06-01 DOI: 10.22108/TOC.2017.102359.1483
T. Mansour, M. Shattuck
{"title":"Combinatorial parameters on bargraphs of permutations","authors":"T. Mansour, M. Shattuck","doi":"10.22108/TOC.2017.102359.1483","DOIUrl":"https://doi.org/10.22108/TOC.2017.102359.1483","url":null,"abstract":"‎In this paper‎, ‎we consider statistics on permutations of length $n$ represented geometrically as bargraphs having the same number of horizontal steps‎. ‎More precisely‎, ‎we find the joint distribution of the descent and up step statistics on the bargraph representations‎, ‎thereby obtaining a new refined count of permutations of a given length‎. ‎To do so‎, ‎we consider the distribution of the parameters on permutations of a more general multiset of which $mathcal{S}_n$ is a subset‎. ‎In addition to finding an explicit formula for the joint distribution on this multiset‎, ‎we provide counts for the total number of descents and up steps of all its members‎, ‎supplying both algebraic and combinatorial proofs‎. ‎Finally‎, ‎we derive explicit expressions for the sign balance of these statistics‎, ‎from which the comparable results on permutations follow as special cases‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"1-16"},"PeriodicalIF":0.4,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48239246","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
On matrix and lattice ideals of digraphs 关于有向图的矩阵和格理想
IF 0.4
Transactions on Combinatorics Pub Date : 2018-06-01 DOI: 10.22108/TOC.2017.105701.1510
Hamid Damadi, F. Rahmati
{"title":"On matrix and lattice ideals of digraphs","authors":"Hamid Damadi, F. Rahmati","doi":"10.22108/TOC.2017.105701.1510","DOIUrl":"https://doi.org/10.22108/TOC.2017.105701.1510","url":null,"abstract":"","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"35-46"},"PeriodicalIF":0.4,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43001934","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
Solution to the minimum harmonic index of graphs with given minimum degree 给定最小度图的最小调和指数的求解
IF 0.4
Transactions on Combinatorics Pub Date : 2018-06-01 DOI: 10.22108/TOC.2017.101076.1462
Meili Liang, Bo Cheng, Jianxi Liu
{"title":"Solution to the minimum harmonic index of graphs with given minimum degree","authors":"Meili Liang, Bo Cheng, Jianxi Liu","doi":"10.22108/TOC.2017.101076.1462","DOIUrl":"https://doi.org/10.22108/TOC.2017.101076.1462","url":null,"abstract":"The harmonic index of a graph G is defined as H(G) = ∑ uv∈E(G) 2 d(u)+d(v) , where d(u) denotes the degree of a vertex u in G. Let G(n, k) be the set of simple n-vertex graphs with minimum degree at least k. In this work we consider the problem of determining the minimum value of the harmonic index and the corresponding extremal graphs among G(n, k). We solve the problem for each integer k(1 ≤ k ≤ n/2) and show the corresponding extremal graph is the complete split graph K∗ k,n−k. This result together with our previous result which solve the problem for each integer k(n/2 ≤ k ≤ n−1) give a complete solution of the problem.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"25-33"},"PeriodicalIF":0.4,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43248343","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
Annihilating submodule graph for modules 模的湮灭子模图
IF 0.4
Transactions on Combinatorics Pub Date : 2018-03-01 DOI: 10.22108/toc.2017.21462
S. Safaeeyan
{"title":"Annihilating submodule graph for modules","authors":"S. Safaeeyan","doi":"10.22108/toc.2017.21462","DOIUrl":"https://doi.org/10.22108/toc.2017.21462","url":null,"abstract":"Let $R$ be a commutative ring and $M$ an‎ ‎$R$-module‎. ‎In this article‎, ‎we introduce a new generalization of‎ ‎the annihilating-ideal graph of commutative rings to modules‎. ‎The‎ ‎annihilating submodule graph of $M$‎, ‎denoted by $Bbb G(M)$‎, ‎is an‎ ‎undirected graph with vertex set $Bbb A^*(M)$ and two distinct‎ ‎elements $N$ and $K$ of $Bbb A^*(M)$ are adjacent if $N*K=0$‎. ‎In‎ ‎this paper we show that $Bbb G(M)$ is a connected graph‎, ‎${rm‎ ‎diam}(Bbb G(M))leq 3$‎, ‎and ${rm gr}(Bbb G(M))leq 4$ if $Bbb‎ ‎G(M)$ contains a cycle‎. ‎Moreover‎, ‎$Bbb G(M)$ is an empty graph‎ ‎if and only if ${rm ann}(M)$ is a prime ideal of $R$ and $Bbb‎ ‎A^*(M)neq Bbb S(M)setminus {0}$ if and only if $M$ is a‎ ‎uniform $R$-module‎, ‎${rm ann}(M)$ is a semi-prime ideal of $R$‎ ‎and $Bbb A^*(M)neq Bbb S(M)setminus {0}$‎. ‎Furthermore‎, ‎$R$‎ ‎is a field if and only if $Bbb G(M)$ is a complete graph‎, ‎for‎ ‎every $Min R-{rm Mod}$‎. ‎If $R$ is a domain‎, ‎for every divisible‎ ‎module $Min R-{rm Mod}$‎, ‎$Bbb G(M)$ is a complete graph with‎ ‎$Bbb A^*(M)=Bbb S(M)setminus {0}$‎. ‎Among other things‎, ‎the‎ ‎properties of a reduced $R$-module $M$ are investigated when‎ ‎$Bbb G(M)$ is a bipartite graph‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"1-12"},"PeriodicalIF":0.4,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47546622","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
PD-sets for codes related to flag-transitive symmetric designs 与标志传递对称设计相关的代码的pd集
IF 0.4
Transactions on Combinatorics Pub Date : 2018-03-01 DOI: 10.22108/TOC.2017.21615
D. Crnković, Nina Mostarac
{"title":"PD-sets for codes related to flag-transitive symmetric designs","authors":"D. Crnković, Nina Mostarac","doi":"10.22108/TOC.2017.21615","DOIUrl":"https://doi.org/10.22108/TOC.2017.21615","url":null,"abstract":"‎For any prime $p$ let $C_p(G)$ be the $p$-ary code spanned by the rows of the incidence matrix $G$ of a graph $Gamma$‎. ‎Let $Gamma$ be the incidence graph of a flag-transitive symmetric design $D$‎. ‎We show that any flag-transitive‎ ‎automorphism group of $D$ can be used as a PD-set for full error correction for the linear code $C_p(G)$‎ ‎(with any information set)‎. ‎It follows that such codes derived from flag-transitive symmetric designs can be‎ ‎decoded using permutation decoding‎. ‎In that way to each flag-transitive symmetric $(v‎, ‎k‎, ‎lambda)$ design we associate a linear code of length $vk$ that is‎ ‎permutation decodable‎. ‎PD-sets obtained in the described way are usually of large cardinality‎. ‎By studying codes arising from some flag-transitive symmetric designs we show that smaller PD-sets can be found for‎ ‎specific information sets‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"37-50"},"PeriodicalIF":0.4,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43763854","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
Products of graphs and Nordhaus-Gaddum type inequalities for eigenvalues 图的乘积与特征值的Nordhaus-Gaddum型不等式
IF 0.4
Transactions on Combinatorics Pub Date : 2018-03-01 DOI: 10.22108/TOC.2017.21474
Nastaran Keyvan, F. Rahmati
{"title":"Products of graphs and Nordhaus-Gaddum type inequalities for eigenvalues","authors":"Nastaran Keyvan, F. Rahmati","doi":"10.22108/TOC.2017.21474","DOIUrl":"https://doi.org/10.22108/TOC.2017.21474","url":null,"abstract":"In this paper, we obtain α as coefficient for the G = Kαn∪K(1−α)n and by which we discuss Nikiforov’s conjecture for λ1 and Aouchiche and Hansen’s conjecture for q1 in Nordhaus-Gaddum type inequalities. Furthermore, by the properties of the products of graphs we put forward a new approach to find some bounds of Nordhaus-Gaddum type inequalities.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"31-36"},"PeriodicalIF":0.4,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45946469","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 harmonic index of subdivision graphs 细分图的调和指数
IF 0.4
Transactions on Combinatorics Pub Date : 2017-12-01 DOI: 10.22108/TOC.2017.21471
B. N. Onagh
{"title":"The harmonic index of subdivision graphs","authors":"B. N. Onagh","doi":"10.22108/TOC.2017.21471","DOIUrl":"https://doi.org/10.22108/TOC.2017.21471","url":null,"abstract":"‎The harmonic index of a graph $G$ is defined as the sum of the weights‎ ‎$frac{2}{deg_G(u)+deg_G(v)}$ of all edges $uv$‎ ‎of $G$‎, ‎where $deg_G(u)$ denotes the degree of a vertex $u$ in $G$‎. ‎In this paper‎, ‎we study the harmonic index of subdivision graphs‎, ‎$t$-subdivision graphs and also‎, ‎$S$-sum and $S_t$-sum of graphs‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"15-27"},"PeriodicalIF":0.4,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41850355","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
On the average eccentricity, the harmonic index and the largest signless Laplacian eigenvalue of a graph 关于图的平均离心率、调和指数和最大无符号拉普拉斯特征值
IF 0.4
Transactions on Combinatorics Pub Date : 2017-12-01 DOI: 10.22108/TOC.2017.21470
H. Deng, S. Balachandran, S. Ayyaswamy, Y. B. Venkatakrishnan
{"title":"On the average eccentricity, the harmonic index and the largest signless Laplacian eigenvalue of a graph","authors":"H. Deng, S. Balachandran, S. Ayyaswamy, Y. B. Venkatakrishnan","doi":"10.22108/TOC.2017.21470","DOIUrl":"https://doi.org/10.22108/TOC.2017.21470","url":null,"abstract":"The eccentricity of a vertex is the maximum distance from it to‎ ‎another vertex and the average eccentricity $eccleft(Gright)$ of a‎ ‎graph $G$ is the mean value of eccentricities of all vertices of‎ ‎$G$‎. ‎The harmonic index $Hleft(Gright)$ of a graph $G$ is defined‎ ‎as the sum of $frac{2}{d_{i}+d_{j}}$ over all edges $v_{i}v_{j}$ of‎ ‎$G$‎, ‎where $d_{i}$ denotes the degree of a vertex $v_{i}$ in $G$‎. ‎In‎ ‎this paper‎, ‎we determine the unique tree with minimum average‎ ‎eccentricity among the set of trees with given number of pendent‎ ‎vertices and determine the unique tree with maximum average‎ ‎eccentricity among the set of $n$-vertex trees with two adjacent‎ ‎vertices of maximum degree $Delta$‎, ‎where $ngeq 2Delta$‎. ‎Also‎, ‎we‎ ‎give some relations between the average eccentricity‎, ‎the harmonic‎ ‎index and the largest signless Laplacian eigenvalue‎, ‎and strengthen‎ ‎a result on the Randi'{c} index and the largest signless Laplacian‎ ‎eigenvalue conjectured by Hansen and Lucas cite{hl}‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"43-50"},"PeriodicalIF":0.4,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47442967","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 central vertices and radius of the regular graph of ideals 理想正则图的中心顶点和半径
IF 0.4
Transactions on Combinatorics Pub Date : 2017-12-01 DOI: 10.22108/TOC.2017.21472
F. Shaveisi
{"title":"The central vertices and radius of the regular graph of ideals","authors":"F. Shaveisi","doi":"10.22108/TOC.2017.21472","DOIUrl":"https://doi.org/10.22108/TOC.2017.21472","url":null,"abstract":"The regular graph of ideals of the commutative ring $R$‎, ‎denoted by ${Gamma_{reg}}(R)$‎, ‎is a graph whose vertex‎ ‎set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element‎. ‎In this paper‎, ‎it is proved that the radius of $Gamma_{reg}(R)$ equals $3$‎. ‎The central vertices of $Gamma_{reg}(R)$ are determined‎, ‎too‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"1-13"},"PeriodicalIF":0.4,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47284918","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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