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Transactions on Combinatorics最新文献

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Splices, Links, and their Edge-Degree Distances 拼接、链接及其边度数距离
IF 0.4
Transactions on Combinatorics Pub Date : 2017-12-01 DOI: 10.22108/TOC.2017.21614
M. Azari, Hojjatollah Divanpour
{"title":"Splices, Links, and their Edge-Degree Distances","authors":"M. Azari, Hojjatollah Divanpour","doi":"10.22108/TOC.2017.21614","DOIUrl":"https://doi.org/10.22108/TOC.2017.21614","url":null,"abstract":"The edge-degree distance of a simple connected graph G is defined as the sum of the terms (d(e|G)+d(f|G))d(e,f|G) over all unordered pairs {e,f} of edges of G, where d(e|G) and d(e,f|G) denote the degree of the edge e in G and the distance between the edges e and f in G, respectively. In this paper, we study the behavior of two versions of the edge-degree distance under two graph products called splice and link.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"29-42"},"PeriodicalIF":0.4,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44548120","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
Some topological indices and graph properties 一些拓扑指标和图的性质
IF 0.4
Transactions on Combinatorics Pub Date : 2017-12-01 DOI: 10.22108/TOC.2017.21467
Xiaomin Zhu, Lihua Feng, Minmin Liu, Weijun Liu, Yuqin Hu
{"title":"Some topological indices and graph properties","authors":"Xiaomin Zhu, Lihua Feng, Minmin Liu, Weijun Liu, Yuqin Hu","doi":"10.22108/TOC.2017.21467","DOIUrl":"https://doi.org/10.22108/TOC.2017.21467","url":null,"abstract":"In this paper, by using the degree sequences of graphs, we present sufficient conditions for a graph to be Hamiltonian, traceable, Hamilton-connected or $k$-connected in light of numerous topological indices such as the eccentric connectivity index, the eccentric distance sum, the connective eccentricity index.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"51-65"},"PeriodicalIF":0.4,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46166700","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
Distance in cayley graphs on permutation groups generated by $k$ $m$-Cycles 由$k$ m$-Cycles生成的置换群上cayley图的距离
IF 0.4
Transactions on Combinatorics Pub Date : 2017-09-01 DOI: 10.22108/TOC.2017.21473
Z. Mostaghim, Mohammad Hossein Ghaffari
{"title":"Distance in cayley graphs on permutation groups generated by $k$ $m$-Cycles","authors":"Z. Mostaghim, Mohammad Hossein Ghaffari","doi":"10.22108/TOC.2017.21473","DOIUrl":"https://doi.org/10.22108/TOC.2017.21473","url":null,"abstract":"In this paper, we extend upon the results of B. Suceavă and R. Stong [Amer. Math. Monthly, 110 (2003) 162–162], which they computed the minimum number of 3-cycles needed to generate an even permutation. Let Ωk,m be the set of all permutations of the form c1c2 · · · ck where ci’s are arbitrary m-cycles in Sn. Suppose that Γ n k,m be the Cayley graph on subgroup of Sn generated by all permutations in Ωk,m. We find a shortest path joining identity and any vertex of Γ n k,m, for arbitrary natural number k, and m = 2, 3, 4. Also, we calculate the diameter of these Cayley graphs. As an application, we present an algorithm for finding a short expression of a permutation as products of given permutations.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"45-59"},"PeriodicalIF":0.4,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47117788","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 hilbert series of binomial edge ideals of generalized trees 关于广义树的二项边理想的hilbert级数
IF 0.4
Transactions on Combinatorics Pub Date : 2017-09-01 DOI: 10.22108/TOC.2017.21463
M. Saeedi, F. Rahmati
{"title":"On the hilbert series of binomial edge ideals of generalized trees","authors":"M. Saeedi, F. Rahmati","doi":"10.22108/TOC.2017.21463","DOIUrl":"https://doi.org/10.22108/TOC.2017.21463","url":null,"abstract":"In this paper we introduce the concept of generalized trees and compute the Hilbert series of their binomial edge ideals‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"11-18"},"PeriodicalIF":0.4,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45458593","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
Common extremal graphs for three inequalities involving domination parameters 涉及控制参数的三个不等式的公共极值图
IF 0.4
Transactions on Combinatorics Pub Date : 2017-09-01 DOI: 10.22108/TOC.2017.21464
V. Samodivkin
{"title":"Common extremal graphs for three inequalities involving domination parameters","authors":"V. Samodivkin","doi":"10.22108/TOC.2017.21464","DOIUrl":"https://doi.org/10.22108/TOC.2017.21464","url":null,"abstract":"‎Let $delta (G)$‎, ‎$Delta (G)$ and $gamma(G)$‎ ‎be the minimum degree‎, ‎maximum degree and‎ ‎domination number of a graph $G=(V(G)‎, ‎E(G))$‎, ‎respectively‎. ‎A partition of $V(G)$‎, ‎all of whose classes are dominating sets in $G$‎, ‎is called a domatic partition of $G$‎. ‎The maximum number of classes of‎ ‎a domatic partition of $G$ is called the domatic number of $G$‎, ‎denoted $d(G)$‎. ‎It is well known that‎ ‎$d(G) leq delta(G)‎ + ‎1$‎, ‎$d(G)gamma(G) leq |V(G)|$ cite{ch}‎, ‎and $|V(G)| leq (Delta(G)‎+‎1)gamma(G)$ cite{berge}‎. ‎In this paper‎, ‎we investigate the graphs $G$ for which‎ ‎all the above inequalities become simultaneously equalities‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"1-9"},"PeriodicalIF":0.4,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42042136","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
Binary sequence/array pairs via diference set pairs: A recursive approach 通过差集对的二进制序列/数组对：一种递归方法
IF 0.4
Transactions on Combinatorics Pub Date : 2017-09-01 DOI: 10.22108/TOC.2017.21466
K. Arasu, Anika Goyal, Abhishek Puri
{"title":"Binary sequence/array pairs via diference set pairs: A recursive approach","authors":"K. Arasu, Anika Goyal, Abhishek Puri","doi":"10.22108/TOC.2017.21466","DOIUrl":"https://doi.org/10.22108/TOC.2017.21466","url":null,"abstract":"Binary array pairs with optimal/ideal correlation values and their algebraic counterparts textquotedblleft difference set pairstextquotedblright;(DSPs) in abelian groups are studied‎. ‎In addition to generalizing known 1-dimensional (sequences) examples‎, ‎we provide four new recursive constructions‎, ‎unifying previously obtained ones‎. ‎Any further advancements in the construction of binary sequences/arrays with optimal/ideal correlation values (equivalently cyclic/abelian difference sets) would give rise to richer classes of DSPs (and hence binary perfect array pairs)‎. ‎Discrete signals arising from DSPs find applications in cryptography‎, ‎CDMA systems‎, ‎radar and wireless communications‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"19-36"},"PeriodicalIF":0.4,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43944944","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 Linear Algorithm for Computing $gamma_{[1,2]}$-set in Generalized Series-Parallel Graphs 广义串并联图中$gamma_{[1,2]}$-集的一种线性算法
IF 0.4
Transactions on Combinatorics Pub Date : 2017-07-01 DOI: 10.22108/TOC.2019.105482.1509
P. Sharifani, M. R. Hooshmandasl
{"title":"A Linear Algorithm for Computing $gamma_{[1,2]}$-set in Generalized Series-Parallel Graphs","authors":"P. Sharifani, M. R. Hooshmandasl","doi":"10.22108/TOC.2019.105482.1509","DOIUrl":"https://doi.org/10.22108/TOC.2019.105482.1509","url":null,"abstract":"For a graph $G=(V,E)$, a set $S subseteq V$ is a $[1,2]$-set if it is a dominating set for $G$ and each vertex $v in V setminus S$ is dominated by at most two vertices of $S$, i.e. $1 leq vert N(v) cap S vert leq 2$. Moreover a set $S subseteq V$ is a total $[1,2]$-set if for each vertex of $V$, it is the case that $1 leq vert N(v) cap S vert leq 2$. The $[1,2]$-domination number of $G$, denoted $gamma_{[1,2]}(G)$, is the minimum number of vertices in a $[1,2]$-set. Every $[1,2]$-set with cardinality of $gamma_{[1,2]}(G)$ is called a $gamma_{[1,2]}$-set. Total $[1,2]$-domination number and $gamma_{t[1,2]}$-sets of $G$ are defined in a similar way. This paper presents a linear time algorithm to find a $gamma_{[1,2]}$-set and a $gamma_{t[1,2]}$-set in generalized series-parallel graphs.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"18 1","pages":"1-24"},"PeriodicalIF":0.4,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78991619","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
Majorization and the number of bipartite graphs for given vertex degrees 给定顶点度的二部图的多数化和数量
IF 0.4
Transactions on Combinatorics Pub Date : 2017-06-08 DOI: 10.22108/TOC.2017.21469
A. Berger
{"title":"Majorization and the number of bipartite graphs for given vertex degrees","authors":"A. Berger","doi":"10.22108/TOC.2017.21469","DOIUrl":"https://doi.org/10.22108/TOC.2017.21469","url":null,"abstract":"The emph{bipartite realisation problem} asks for a pair of non-negative‎, ‎non-increasing integer lists $a:=(a_1,ldots,a_n)$ and $b:=(b_1,ldots,b_{n'})$ if there is a labeled bipartite graph $G(U,V,E)$ (no loops or multiple edges) such that each vertex $u_i in U$ has degree $a_i$ and each vertex $v_i in V$ degree $b_i.$ The Gale-Ryser theorem provides characterisations for the existence of a `realisation' $G(U,V,E)$ that are strongly related to the concept of emph{majorisation}‎. ‎We prove a generalisation; list pair $(a,b)$ has more realisations than $(a',b),$ if $a'$ majorises $a.$ Furthermore‎, ‎we give explicitly list pairs which possess the largest number of realisations under all $(a,b)$ with fixed $n$‎, ‎$n'$ and $m:=sum_{i=1}^n a_i.$ We introduce the notion~emph{minconvex list pairs} for them‎. ‎If $n$ and $n'$ divide $m,$ minconvex list pairs turn in the special case of two constant lists $a=(frac{m}{n},ldots,frac{m}{n})$ and $b=(frac{m}{n'},ldots,frac{m}{n'}).$‎","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"60 1","pages":"19-30"},"PeriodicalIF":0.4,"publicationDate":"2017-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68209137","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
On numerical semigroups with embedding dimension three 关于嵌入维数为3的数值半群
IF 0.4
Transactions on Combinatorics Pub Date : 2017-06-01 DOI: 10.22108/TOC.2017.20736
A. Mahdavi, F. Rahmati
{"title":"On numerical semigroups with embedding dimension three","authors":"A. Mahdavi, F. Rahmati","doi":"10.22108/TOC.2017.20736","DOIUrl":"https://doi.org/10.22108/TOC.2017.20736","url":null,"abstract":"Let $fneq1,3$ be a positive integer‎. ‎We prove that there exists a numerical semigroup $S$ with embedding dimension three such that $f$ is the Frobenius number of $S$‎. ‎We also show that‎ ‎the same fact holds for affine semigroups in higher dimensional monoids‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"1-6"},"PeriodicalIF":0.4,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44754241","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: 14
Full edge-friendly index sets of complete bipartite graphs 完备二部图的满边友好索引集
IF 0.4
Transactions on Combinatorics Pub Date : 2017-06-01 DOI: 10.22108/TOC.2017.20739
W. Shiu
{"title":"Full edge-friendly index sets of complete bipartite graphs","authors":"W. Shiu","doi":"10.22108/TOC.2017.20739","DOIUrl":"https://doi.org/10.22108/TOC.2017.20739","url":null,"abstract":"‎‎Let $G=(V,E)$ be a simple graph‎. ‎An edge labeling $f:Eto {0,1}$ induces a vertex labeling $f^+:VtoZ_2$ defined by $f^+(v)equiv sumlimits_{uvin E} f(uv)pmod{2}$ for each $v in V$‎, ‎where $Z_2={0,1}$ is the additive group of order 2‎. ‎For $iin{0,1}$‎, ‎let‎ ‎$e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$‎. ‎A labeling $f$ is called edge-friendly if‎ ‎$|e_f(1)-e_f(0)|le 1$‎. ‎$I_f(G)=v_f(1)-v_f(0)$ is called the edge-friendly index of $G$ under an edge-friendly labeling $f$‎. ‎The full edge-friendly index set of a graph $G$ is the set of all possible edge-friendly indices of $G$‎. ‎Full edge-friendly index sets of complete bipartite graphs will be determined‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"7-17"},"PeriodicalIF":0.4,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42808078","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
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