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Transactions on Combinatorics最新文献

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On the minimum stopping sets of product codes 关于产品代码的最小停止集
IF 0.4
Transactions on Combinatorics Pub Date : 2018-12-01 DOI: 10.22108/TOC.2017.101199.1465
M. Hivadi, Akbar Zare Chavoshi
{"title":"On the minimum stopping sets of product codes","authors":"M. Hivadi, Akbar Zare Chavoshi","doi":"10.22108/TOC.2017.101199.1465","DOIUrl":"https://doi.org/10.22108/TOC.2017.101199.1465","url":null,"abstract":"It is shown that the certain combinatorial structures called stopping sets have the important role in analysis of iterative decoding. In this paper, the number of minimum stopping sets of a product code is determined by the number of the minimum stopping sets of the corresponding component codes. As an example, the number of minimum stopping sets of the r-dimensional SPC product code is computed.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"1-6"},"PeriodicalIF":0.4,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42520073","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 $1$-factorizability of quartic supersolvable Cayley graphs 关于四次超可解Cayley图的$1$可分解性的一个注记
IF 0.4
Transactions on Combinatorics Pub Date : 2018-12-01 DOI: 10.22108/TOC.2018.104578.1500
M. Ahanjideh, A. Iranmanesh
{"title":"A note on $1$-factorizability of quartic supersolvable Cayley graphs","authors":"M. Ahanjideh, A. Iranmanesh","doi":"10.22108/TOC.2018.104578.1500","DOIUrl":"https://doi.org/10.22108/TOC.2018.104578.1500","url":null,"abstract":"Alspach et al‎. ‎conjectured that every quartic Cayley graph on an even solvable group is $1$-factorizable‎. ‎In this paper‎, ‎we verify this conjecture for quartic Cayley graphs on supersolvable groups of even order‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"7-10"},"PeriodicalIF":0.4,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46800278","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
Directed zero-divisor graph and skew power series rings 有向零因子图与斜幂级数环
IF 0.4
Transactions on Combinatorics Pub Date : 2018-12-01 DOI: 10.22108/TOC.2018.109048.1543
E. Hashemi, Marzieh Yazdanfar, A. Alhevaz
{"title":"Directed zero-divisor graph and skew power series rings","authors":"E. Hashemi, Marzieh Yazdanfar, A. Alhevaz","doi":"10.22108/TOC.2018.109048.1543","DOIUrl":"https://doi.org/10.22108/TOC.2018.109048.1543","url":null,"abstract":"‎Let $R$ be an associative ring with identity and $Z^{ast}(R)$ be its set of non-zero zero-divisors‎. ‎Zero-divisor graphs of rings are well represented in the literature of commutative and non-commutative rings‎. ‎The directed zero-divisor graph of $R$‎, ‎denoted by $Gamma{(R)}$‎, ‎is the directed graph whose vertices are the set of non-zero zero-divisors of $R$ and for distinct non-zero zero-divisors $x,y$‎, ‎$xrightarrow y$ is an directed edge if and only if $xy=0$‎. ‎In this paper‎, ‎we connect some graph-theoretic concepts with algebraic notions‎, ‎and investigate the interplay between the ring-theoretical properties of a skew power series ring $R[[x;alpha]]$ and the graph-theoretical properties of its directed zero-divisor graph $Gamma(R[[x;alpha]])$‎. ‎In doing so‎, ‎we give a characterization of the possible diameters of $Gamma(R[[x;alpha]])$ in terms of the diameter of $Gamma(R)$‎, ‎when the base ring $R$ is reversible and right Noetherian with an‎ ‎$alpha$-condition‎, ‎namely $alpha$-compatible property‎. ‎We also provide many examples for showing the necessity of our assumptions‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"43-57"},"PeriodicalIF":0.4,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41692683","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
Degree resistance distance of trees with some given parameters 给定参数下树的度阻力距离
IF 0.4
Transactions on Combinatorics Pub Date : 2018-12-01 DOI: 10.22108/TOC.2018.108656.1538
Fangguo He, Xinnong Jiang
{"title":"Degree resistance distance of trees with some given parameters","authors":"Fangguo He, Xinnong Jiang","doi":"10.22108/TOC.2018.108656.1538","DOIUrl":"https://doi.org/10.22108/TOC.2018.108656.1538","url":null,"abstract":"The degree resistance distance of a graph $G$ is defined as $D_R(G)=sum_{i<j}(d(v_i)+d(v_j))R(v_i,v_j)$, where $d(v_i)$ is the degree of the vertex $v_i$, and $R(v_i,v_j)$ is the resistance distance between the vertices $v_i$ and $v_j$. Here we characterize the extremal graphs with respect to degree resistance distance among trees with given diameter, number of pendent vertices, independence number, covering number, and maximum degree, respectively.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"11-24"},"PeriodicalIF":0.4,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48198784","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
Iota energy of weighted digraphs 加权有向图的Iota能量
IF 0.4
Transactions on Combinatorics Pub Date : 2018-09-01 DOI: 10.22108/TOC.2018.109248.1546
S. Hafeez, Mehtab Khan
{"title":"Iota energy of weighted digraphs","authors":"S. Hafeez, Mehtab Khan","doi":"10.22108/TOC.2018.109248.1546","DOIUrl":"https://doi.org/10.22108/TOC.2018.109248.1546","url":null,"abstract":"","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"55-73"},"PeriodicalIF":0.4,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48468989","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 annihilator graph of a 0-distributive lattice 0-分配格的零化子图
IF 0.4
Transactions on Combinatorics Pub Date : 2018-09-01 DOI: 10.22108/TOC.2017.104919.1507
S. Bagheri, Mahtab Koohi Kerahroodi
{"title":"The annihilator graph of a 0-distributive lattice","authors":"S. Bagheri, Mahtab Koohi Kerahroodi","doi":"10.22108/TOC.2017.104919.1507","DOIUrl":"https://doi.org/10.22108/TOC.2017.104919.1507","url":null,"abstract":"‎‎In this article‎, ‎for a lattice $mathcal L$‎, ‎we define and investigate‎ ‎the annihilator graph $mathfrak {ag} (mathcal L)$ of $mathcal L$ which contains the zero-divisor graph of $mathcal L$ as a subgraph‎. ‎Also‎, ‎for a 0-distributive lattice $mathcal L$‎, ‎we study some properties of this graph such as regularity‎, ‎connectedness‎, ‎the diameter‎, ‎the girth and its domination number‎. ‎Moreover‎, ‎for a distributive lattice $mathcal L$ with $Z(mathcal L)neqlbrace 0rbrace$‎, ‎we show that $mathfrak {ag} (mathcal L) = Gamma(mathcal L)$ if and only if $mathcal L$ has exactly two minimal prime ideals‎. ‎Among other things‎, ‎we consider the annihilator graph $mathfrak {ag} (mathcal L)$ of the lattice $mathcal L=(mathcal D(n),|)$ containing all positive divisors of a non-prime natural number $n$ and we compute some invariants such as the domination number‎, ‎the clique number and the chromatic number of this graph‎. ‎Also‎, ‎for this lattice we investigate some special cases in which $mathfrak {ag} (mathcal D(n))$ or $Gamma(mathcal D(n))$ are planar‎, ‎Eulerian or Hamiltonian.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"1-18"},"PeriodicalIF":0.4,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48832969","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
$mathcal{B}$-Partitions, determinant and permanent of graphs $mathcal｛B｝$-图的分块、行列式和永久性
IF 0.4
Transactions on Combinatorics Pub Date : 2018-09-01 DOI: 10.22108/TOC.2017.105288.1508
R. Singh, R. Bapat
{"title":"$mathcal{B}$-Partitions, determinant and permanent of graphs","authors":"R. Singh, R. Bapat","doi":"10.22108/TOC.2017.105288.1508","DOIUrl":"https://doi.org/10.22108/TOC.2017.105288.1508","url":null,"abstract":"Let $G$ be a graph (directed or undirected) having $k$ number of blocks $B_1, B_2,hdots,B_k$. A $mathcal{B}$-partition of $G$ is a partition consists of $k$ vertex-disjoint subgraph $(hat{B_1},hat{B_1},hdots,hat{B_k})$ such that $hat{B}_i$ is an induced subgraph of $B_i$ for $i=1,2,hdots,k.$ The terms $prod_{i=1}^{k}det(hat{B}_i), prod_{i=1}^{k}text{per}(hat{B}_i)$ represent the det-summands and the per-summands, respectively, corresponding to the $mathcal{B}$-partition $(hat{B_1},hat{B_1},hdots,hat{B_k})$. The determinant (permanent) of a graph having no loops on its cut-vertices is equal to the summation of the det-summands (per-summands), corresponding to all possible $mathcal{B}$-partitions. In this paper, we calculate the determinant and the permanent of classes of graphs such as block graph, block graph with negatives cliques, signed unicyclic graph, mixed complete graph, negative mixed complete graph, and star mixed block graphs.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"37-54"},"PeriodicalIF":0.4,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45959697","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
Sufficient conditions for triangle-free graphs to be super-$λ'$ 无三角图是超λ的充分条件
IF 0.4
Transactions on Combinatorics Pub Date : 2018-09-01 DOI: 10.22108/TOC.2018.106623.1523
Huiwen Cheng, Yanjun Li
{"title":"Sufficient conditions for triangle-free graphs to be super-$λ'$","authors":"Huiwen Cheng, Yanjun Li","doi":"10.22108/TOC.2018.106623.1523","DOIUrl":"https://doi.org/10.22108/TOC.2018.106623.1523","url":null,"abstract":"","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"29-36"},"PeriodicalIF":0.4,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47405374","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 spectral excess theorem for digraphs with normal Laplacian matrices 具有正规拉普拉斯矩阵的有向图的谱过剩定理
IF 0.4
Transactions on Combinatorics Pub Date : 2018-09-01 DOI: 10.22108/TOC.2018.105873.1513
F. Shafiei
{"title":"A spectral excess theorem for digraphs with normal Laplacian matrices","authors":"F. Shafiei","doi":"10.22108/TOC.2018.105873.1513","DOIUrl":"https://doi.org/10.22108/TOC.2018.105873.1513","url":null,"abstract":"The spectral excess theorem‎, ‎due to Fiol and Garriga in 1997‎, ‎is an important result‎, ‎because it gives a good characterization‎ ‎of distance-regularity in graphs‎. ‎Up to now‎, ‎some authors have given some variations of this theorem‎. ‎Motivated by this‎, ‎we give the corresponding result by using the Laplacian spectrum for digraphs‎. ‎We also illustrate this Laplacian spectral excess theorem for digraphs with few Laplacian eigenvalues and we show that any strongly connected and regular digraph that has normal Laplacian matrix with three distinct eigenvalues‎, ‎is distance-regular‎. ‎Hence such a digraph is strongly regular with girth $g=2$ or $g=3$‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"19-28"},"PeriodicalIF":0.4,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45096002","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
Reduced zero-divisor graphs of posets 偏集的约简零因子图
IF 0.4
Transactions on Combinatorics Pub Date : 2018-06-01 DOI: 10.22108/toc.2018.55164.1417
Deiborlang Nongsiang, P. K. Saikia
{"title":"Reduced zero-divisor graphs of posets","authors":"Deiborlang Nongsiang, P. K. Saikia","doi":"10.22108/toc.2018.55164.1417","DOIUrl":"https://doi.org/10.22108/toc.2018.55164.1417","url":null,"abstract":"","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"7 1","pages":"47-54"},"PeriodicalIF":0.4,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48805238","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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