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The site-perimeter of words 文字的站点边界
IF 0.4
Transactions on Combinatorics Pub Date : 2017-06-01 DOI: 10.22108/TOC.2017.21465
A. Blecher, C. Brennan, A. Knopfmacher, T. Mansour
{"title":"The site-perimeter of words","authors":"A. Blecher, C. Brennan, A. Knopfmacher, T. Mansour","doi":"10.22108/TOC.2017.21465","DOIUrl":"https://doi.org/10.22108/TOC.2017.21465","url":null,"abstract":"","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"37-48"},"PeriodicalIF":0.4,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45417774","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
A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs 欧拉双向图上Bouchet猜想有效性的新证明
IF 0.4
Transactions on Combinatorics Pub Date : 2017-06-01 DOI: 10.22108/TOC.2017.21362
N. Ghareghani
{"title":"A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs","authors":"N. Ghareghani","doi":"10.22108/TOC.2017.21362","DOIUrl":"https://doi.org/10.22108/TOC.2017.21362","url":null,"abstract":"Recently, E. M'{a}v{c}ajov'{a} and M. v{S}koviera proved that every bidirected Eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. This result shows the validity of Bouchet's nowhere zero conjecture for Eulerian bidirected graphs. In this paper we prove the same theorem in a different terminology and with a short and simple proof. More precisely, we prove that every Eulerian undirected graph which admits a zero-sum flow, admits a zero-sum $4$-flow. As a conclusion we obtain a shorter proof for the previously mentioned result of M'{a}v{c}ajov'{a} and v{S}koviera.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"31-35"},"PeriodicalIF":0.4,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45759654","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
Adjacent vertex distinguishing acyclic edge coloring of the Cartesian product of graphs 图的笛卡尔积的无环边着色的邻顶点区分
IF 0.4
Transactions on Combinatorics Pub Date : 2017-06-01 DOI: 10.22108/TOC.2017.20988
F. S. Mousavi, M. Noori
{"title":"Adjacent vertex distinguishing acyclic edge coloring of the Cartesian product of graphs","authors":"F. S. Mousavi, M. Noori","doi":"10.22108/TOC.2017.20988","DOIUrl":"https://doi.org/10.22108/TOC.2017.20988","url":null,"abstract":"‎Let $G$ be a graph and $chi^{prime}_{aa}(G)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $G$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎We prove a general bound for $chi^{prime}_{aa}(Gsquare H)$ for any two graphs $G$ and $H$‎. ‎We also determine‎ ‎exact value of this parameter for the Cartesian product of two paths‎, ‎Cartesian product of a path and a cycle‎, ‎Cartesian product of two trees‎, ‎hypercubes‎. ‎We show that $chi^{prime}_{aa}(C_msquare C_n)$ is at most $6$ fo every $mgeq 3$ and $ngeq 3$‎. ‎Moreover in some cases we find the exact value of $chi^{prime}_{aa}(C_msquare C_n)$‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"19-30"},"PeriodicalIF":0.4,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45759862","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 annihilator graph of a finite commutative ring 有限交换环的湮灭子图
IF 0.4
Transactions on Combinatorics Pub Date : 2017-03-01 DOI: 10.22108/TOC.2017.20360
Sanghita Dutta, Chanlemki Lanong
{"title":"On annihilator graph of a finite commutative ring","authors":"Sanghita Dutta, Chanlemki Lanong","doi":"10.22108/TOC.2017.20360","DOIUrl":"https://doi.org/10.22108/TOC.2017.20360","url":null,"abstract":"‎The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the vertex set $Z(R)^*$ and two distinct vertices are adjacent if and only if $ann(x) cup ann(y)$ $ neq $ $ann(xy)$‎. ‎In this paper we give the sufficient condition for a graph $AG(R)$ to be complete‎. ‎We characterize rings for which $AG(R)$ is a regular graph‎, ‎we show that $gamma (AG(R))in {1,2}$ and we also characterize the rings for which $AG(R)$ has a cut vertex‎. ‎Finally we find the clique number of a finite reduced ring and characterize the rings for which $AG(R)$ is a planar graph‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"1-11"},"PeriodicalIF":0.4,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41657412","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
A neighborhood union condition for fractional $(k,n',m)$-critical deleted graphs 分数阶$(k,n'，m)$-临界删除图的邻域联合条件
IF 0.4
Transactions on Combinatorics Pub Date : 2017-03-01 DOI: 10.22108/TOC.2017.20355
Yun Gao, M. Farahani, Wei Gao
{"title":"A neighborhood union condition for fractional $(k,n',m)$-critical deleted graphs","authors":"Yun Gao, M. Farahani, Wei Gao","doi":"10.22108/TOC.2017.20355","DOIUrl":"https://doi.org/10.22108/TOC.2017.20355","url":null,"abstract":"A graph $G$ is called a fractional‎ ‎$(k,n',m)$-critical deleted graph if any $n'$ vertices are removed‎ ‎from $G$ the resulting graph is a fractional $(k,m)$-deleted‎ ‎graph‎. ‎In this paper‎, ‎we prove that for integers $kge 2$‎, ‎$n',mge0$‎, ‎$nge8k+n'+4m-7$‎, ‎and $delta(G)ge k+n'+m$‎, ‎if‎ ‎$$|N_{G}(x)cup N_{G}(y)|gefrac{n+n'}{2}$$‎ ‎for each pair of non-adjacent vertices $x$‎, ‎$y$ of $G$‎, ‎then $G$‎ ‎is a fractional $(k,n',m)$-critical deleted graph‎. ‎The bounds for‎ ‎neighborhood union condition‎, ‎the order $n$ and the minimum degree‎ ‎$delta(G)$ of $G$ are all sharp‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"13-19"},"PeriodicalIF":0.4,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45056139","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: 7
The condition for a sequence to be potentially $A_{L, M}$- graphic 一个序列可能是$A_{L, M}$-图形的条件
IF 0.4
Transactions on Combinatorics Pub Date : 2017-03-01 DOI: 10.22108/TOC.2017.20361
S. Pirzada, Bilal A. Chat
{"title":"The condition for a sequence to be potentially $A_{L, M}$- graphic","authors":"S. Pirzada, Bilal A. Chat","doi":"10.22108/TOC.2017.20361","DOIUrl":"https://doi.org/10.22108/TOC.2017.20361","url":null,"abstract":"The set of all non-increasing non-negative integer sequences $pi=(d_1‎, ‎d_2,ldots,d_n)$ is denoted by $NS_n$‎. ‎A sequence $piin NS_{n}$ is said to be graphic if it is the degree sequence of a simple graph $G$ on $n$ vertices‎, ‎and such a graph $G$ is called a realization of $pi$‎. ‎The set of all graphic sequences in $NS_{n}$ is denoted by $GS_{n}$‎. ‎The complete product split graph on $L‎ + ‎M$ vertices is denoted by $overline{S}_{L‎, ‎M}=K_{L} vee overline{K}_{M}$‎, ‎where $K_{L}$ and $K_{M}$ are complete graphs respectively on $L = sumlimits_{i = 1}^{p}r_{i}$ and $M = sumlimits_{i = 1}^{p}s_{i}$ vertices with $r_{i}$ and $s_{i}$ being integers‎. ‎Another split graph is denoted by $S_{L‎, ‎M} = overline{S}_{r_{1}‎, ‎s_{1}} veeoverline{S}_{r_{2}‎, ‎s_{2}} vee cdots vee overline{S}_{r_{p}‎, ‎s_{p}}= (K_{r_{1}} vee overline{K}_{s_{1}})vee (K_{r_{2}} vee overline{K}_{s_{2}})vee cdots vee (K_{r_{p}} vee overline{K}_{s_{p}})$‎. ‎A sequence $pi=(d_{1}‎, ‎d_{2},ldots,d_{n})$ is said to be potentially $S_{L‎, ‎M}$-graphic (respectively $overline{S}_{L‎, ‎M}$)-graphic if there is a realization $G$ of $pi$ containing $S_{L‎, ‎M}$ (respectively $overline{S}_{L‎, ‎M}$) as a subgraph‎. ‎If $pi$ has a realization $G$ containing $S_{L‎, ‎M}$ on those vertices having degrees $d_{1}‎, ‎d_{2},ldots,d_{L+M}$‎, ‎then $pi$ is potentially $A_{L‎, ‎M}$-graphic‎. ‎A non-increasing sequence of non-negative integers $pi = (d_{1}‎, ‎d_{2},ldots,d_{n})$ is potentially $A_{L‎, ‎M}$-graphic if and only if it is potentially $S_{L‎, ‎M}$-graphic‎. ‎In this paper‎, ‎we obtain the sufficient condition for a graphic sequence to be potentially $A_{L‎, ‎M}$-graphic and this result is a generalization of that given by J‎. ‎H‎. ‎Yin on split graphs‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"21-27"},"PeriodicalIF":0.4,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42635835","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 skew spectral moments of graphs 关于图的偏谱矩
IF 0.4
Transactions on Combinatorics Pub Date : 2017-03-01 DOI: 10.22108/TOC.2017.20737
F. Taghvaee, G. Fath-Tabar
{"title":"On the skew spectral moments of graphs","authors":"F. Taghvaee, G. Fath-Tabar","doi":"10.22108/TOC.2017.20737","DOIUrl":"https://doi.org/10.22108/TOC.2017.20737","url":null,"abstract":"Let $G$ be a simple graph‎, ‎and $G^{sigma}$‎ ‎be an oriented graph of $G$ with the orientation ‎$sigma$ and skew-adjacency matrix $S(G^{sigma})$‎. ‎The $k-$th skew spectral‎ ‎moment of $G^{sigma}$‎, ‎denoted by‎ ‎$T_k(G^{sigma})$‎, ‎is defined as $sum_{i=1}^{n}( ‎‎‎lambda_{i})^{k}$‎, ‎where $lambda_{1}‎, ‎lambda_{2},cdots‎, ‎lambda_{n}$ are the eigenvalues of $G^{sigma}$‎. ‎Suppose‎ ‎$G^{sigma_1}_{1}$ and $G^{sigma_2}_{2}$ are two digraphs‎. ‎If there‎ ‎exists an integer $k$‎, ‎$1 leq k leq n-1$‎, ‎such that for each‎ ‎$i$‎, ‎$0 leq i leq k-1$‎, ‎$T_i(G^{sigma_1}_{1}) =‎ ‎T_i(G^{sigma_2}_{2})$ and‎ ‎$T_k(G^{sigma_1}_{1}) <T_k(G^{sigma_ 2}_{2})$‎ ‎then we write‎ ‎$G^{sigma_1}_{1} prec_{T} G^{sigma_2}_{2}$‎. ‎In this paper‎, ‎we determine some of the skew spectral moments of oriented graphs‎. ‎Also we order some oriented unicyclic graphs with respect to skew spectral moment‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"47-54"},"PeriodicalIF":0.4,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45734128","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 properties of comaximal ideal graph of a commutative ring 交换环的共模理想图的一些性质
IF 0.4
Transactions on Combinatorics Pub Date : 2017-03-01 DOI: 10.22108/TOC.2017.20429
Z. Jafari, M. Azadi
{"title":"Some properties of comaximal ideal graph of a commutative ring","authors":"Z. Jafari, M. Azadi","doi":"10.22108/TOC.2017.20429","DOIUrl":"https://doi.org/10.22108/TOC.2017.20429","url":null,"abstract":"Let $R$ be a commutative ring with identity‎. ‎We use‎ ‎$varphi (R)$ to denote the comaximal ideal graph‎. ‎The vertices‎ ‎of $varphi (R)$ are proper ideals of R which are not contained‎ ‎in the Jacobson radical of $R$‎, ‎and two vertices $I$ and $J$ are‎ ‎adjacent if and only if $I‎ + ‎J = R$‎. ‎In this paper we show some‎ ‎properties of this graph together with planarity of line graph‎ ‎associated to $varphi (R)$‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"29-37"},"PeriodicalIF":0.4,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46880714","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
A family of $t$-regular self-complementary $k$-hypergraphs 一组$t$-正则自互补$k$-超图
IF 0.4
Transactions on Combinatorics Pub Date : 2017-03-01 DOI: 10.22108/TOC.2017.20363
M. Ariannejad, M. Emami, O. Naserian
{"title":"A family of $t$-regular self-complementary $k$-hypergraphs","authors":"M. Ariannejad, M. Emami, O. Naserian","doi":"10.22108/TOC.2017.20363","DOIUrl":"https://doi.org/10.22108/TOC.2017.20363","url":null,"abstract":"We use the recursive method of construction large sets of t-designs given by Qiu-rong Wu (A note on extending t-designs‎, ‎{em Australas‎. ‎J‎. ‎Combin.}‎, ‎{bf 4} (1991) 229--235.), and present a similar method for constructing $t$-subset-regular‎ ‎self-complementary $k$-uniform hypergraphs of order $v$‎. ‎As an‎ ‎application we show the existence of a new family of 2-subset-regular‎ ‎self-complementary 4-uniform hypergraphs with $v=16m+3$‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"39-46"},"PeriodicalIF":0.4,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46547985","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
CONGRUENCES FROM Q-CATALAN IDENTITIES q -加泰罗尼亚恒等式的同余
IF 0.4
Transactions on Combinatorics Pub Date : 2016-12-01 DOI: 10.22108/TOC.2016.20358
Qing Zou
{"title":"CONGRUENCES FROM Q-CATALAN IDENTITIES","authors":"Qing Zou","doi":"10.22108/TOC.2016.20358","DOIUrl":"https://doi.org/10.22108/TOC.2016.20358","url":null,"abstract":"In this paper‎, ‎by studying three $q$-Catalan identities given by Andrews‎, ‎we arrive at a certain number of congruences‎. ‎These congruences are all modulo $Phi_n(q)$‎, ‎the $n$-th cyclotomic polynomial or the related functions and modulo $q$-integers‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"57-67"},"PeriodicalIF":0.4,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208555","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: 5
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