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An effective new heuristic algorithm for solving permutation flow shop scheduling problem 求解置换流水车间调度问题的一种有效的启发式算法
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-30 DOI: 10.22108/TOC.2021.126406.1795
S. F. Rad.
{"title":"An effective new heuristic algorithm for solving permutation flow shop scheduling problem","authors":"S. F. Rad.","doi":"10.22108/TOC.2021.126406.1795","DOIUrl":"https://doi.org/10.22108/TOC.2021.126406.1795","url":null,"abstract":"The deterministic permutation flow shop scheduling problem with makespan criterion is not solvable in polynomial time‎. ‎Therefore‎, ‎researchers have thought about heuristic algorithms‎. ‎There are many heuristic algorithms for solving it that is a very important combinatorial optimization problem‎. ‎In this paper‎, ‎a new algorithm is proposed for solving the mentioned problem‎. ‎The presented algorithm chooses the weighted path that starts from the up-left corner and reaches the down-right in the matrix of jobs processing times and calculates the biggest sum of the times in the footprints of this path‎. ‎The row with the biggest sum permutes among all the rows of the matrix for locating the minimum of makespan‎. ‎This method was run on Taillard’s standard benchmark and the solutions were compared with the optimum or the best ones as well as 14 famous heuristics‎. ‎The validity and effectiveness of the algorithm are shown with tables and statistical evaluation‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43037981","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 local core number based algorithm for the maximum clique problem 最大集团问题的一种基于局部核数的算法
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-21 DOI: 10.22108/TOC.2021.120153.1686
Neda Mohammadi, M. Kadivar
{"title":"A local core number based algorithm for the maximum clique problem","authors":"Neda Mohammadi, M. Kadivar","doi":"10.22108/TOC.2021.120153.1686","DOIUrl":"https://doi.org/10.22108/TOC.2021.120153.1686","url":null,"abstract":"The maximum clique problem (MCP) is to determine a complete subgraph of maximum cardinality in a graph. MCP is a fundamental problem in combinatorial optimization and is noticeable for its wide range of applications. In this paper, we present two branch-and-bound exact algorithms for finding a maximum clique in an undirected graph. Many efficient exact branch and bound maximum clique algorithms use approximate coloring to compute an upper bound on the clique number but, as a new pruning strategy, we show that local core numbers are more efficient. Moreover, instead of neighbors set of a vertex, our search area is restricted to a subset of the set in each subproblem which speeds up clique finding process. This subset is based on the core of the vertices of a given graph. We improved the MCQ and MaxCliqueDyn algorithms with respect to the new pruning strategy and search area restriction. Experimental results demonstrate that the improved algorithms outperform the previous well-known algorithms for many instances when applied to DIMACS benchmark and random graphs.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45909661","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
Vertex decomposability of complexes associated to forests 森林复合体的顶点可分解性
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-14 DOI: 10.22108/TOC.2021.127059.1809
Anurag Singh
{"title":"Vertex decomposability of complexes associated to forests","authors":"Anurag Singh","doi":"10.22108/TOC.2021.127059.1809","DOIUrl":"https://doi.org/10.22108/TOC.2021.127059.1809","url":null,"abstract":"In this article‎, ‎we discuss the vertex decomposability of three well-studied simplicial complexes associated to forests‎. ‎In particular‎, ‎we show that the bounded degree complex of a forest and the complex of directed trees of a multidiforest is vertex decomposable‎. ‎We then prove that the non-cover complex of a forest is either contractible or homotopy equivalent to a sphere‎. ‎Finally we provide a complete characterization of forests whose non-cover complexes are vertex decomposable‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49303969","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
Upper bounds for the reduced second zagreb index of graphs 图的约化第二萨格勒布索引的上界
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-01 DOI: 10.22108/TOC.2020.125478.1774
B. Horoldagva, Tsend-Ayush Selenge, Lkhagva Buyantogtokh, Shiikhar Dorjsembe
{"title":"Upper bounds for the reduced second zagreb index of graphs","authors":"B. Horoldagva, Tsend-Ayush Selenge, Lkhagva Buyantogtokh, Shiikhar Dorjsembe","doi":"10.22108/TOC.2020.125478.1774","DOIUrl":"https://doi.org/10.22108/TOC.2020.125478.1774","url":null,"abstract":"The graph invariant $RM_2$‎, ‎known under the name reduced second Zagreb index‎, ‎is defined as $RM_2(G)=sum_{uvin E(G)}(d_G(u)-1)(d_G(v)-1)$‎, ‎where $d_G(v)$ is the degree of the vertex $v$ of the graph $G$‎. ‎In this paper‎, ‎we give a tight upper bound of $RM_2$ for the class of graphs of order $n$ and size $m$ with at least one dominating vertex‎. ‎Also‎, ‎we obtain sharp upper bounds on $RM_2$ for all graphs of order $n$ with $k$ dominating vertices and for all graphs of order $n$ with $k$ pendant vertices‎. ‎Finally‎, ‎we give a sharp upper bound on $RM_2$ for all $k$-apex trees of order $n$‎. ‎Moreover‎, ‎the corresponding extremal graphs are characterized‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"10 1","pages":"137-148"},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208739","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 finite groups all of whose bi-Cayley graphs of bounded valency are integral 在有限群上，所有有界价的双凯利图都是积分的
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-01 DOI: 10.22108/TOC.2021.126275.1787
M. Arezoomand
{"title":"On finite groups all of whose bi-Cayley graphs of bounded valency are integral","authors":"M. Arezoomand","doi":"10.22108/TOC.2021.126275.1787","DOIUrl":"https://doi.org/10.22108/TOC.2021.126275.1787","url":null,"abstract":"Let $kgeq 1$ be an integer and $mathcal{I}_k$ be‎ ‎the set of all finite groups $G$ such that every bi-Cayley graph $BCay(G,S)$ of $G$ with respect to‎ ‎subset $S$ of length $1leq |S|leq k$ is integral‎. ‎Let $kgeq 3$‎. ‎We prove that a finite group $G$ belongs to $mathcal{I}_k$ if and‎ ‎only if $GcongBbb Z_3$‎, ‎$Bbb Z_2^r$ for some integer $r$‎, ‎or $S_3$‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"10 1","pages":"247-252"},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208855","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
Convolution identities involving the central binomial coefficients and Catalan numbers 涉及中心二项式系数和加泰罗尼亚数的卷积恒等式
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-01 DOI: 10.22108/TOC.2021.127505.1821
Necdet Batır, Hakan Küçük, Sezer Sorgun
{"title":"Convolution identities involving the central binomial coefficients and Catalan numbers","authors":"Necdet Batır, Hakan Küçük, Sezer Sorgun","doi":"10.22108/TOC.2021.127505.1821","DOIUrl":"https://doi.org/10.22108/TOC.2021.127505.1821","url":null,"abstract":"We generalize some convolution identities due to Witula and Qi et al‎. ‎involving the central binomial coefficients and Catalan numbers‎. ‎Our formula allows us to establish many new identities involving these important quantities‎, ‎and recovers some known identities in the literature‎. ‎Also‎, ‎we give new proofs of Shapiro's Catalan convolution and a famous identity of Haj'{o}s‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"10 1","pages":"225-238"},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208903","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 the extremal connective eccentricity index among trees with maximum degree 最大度树间的极端连接偏心指数
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-01 DOI: 10.22108/TOC.2021.120679.1693
Fazal Hayat
{"title":"On the extremal connective eccentricity index among trees with maximum degree","authors":"Fazal Hayat","doi":"10.22108/TOC.2021.120679.1693","DOIUrl":"https://doi.org/10.22108/TOC.2021.120679.1693","url":null,"abstract":"The connective eccentricity index (CEI) of a graph $G$ is defined as $xi^{ce}(G)=sum_{v in V(G)}frac{d_G(v)}{varepsilon_G(v)}$, where $d_G(v)$ is the degree of $v$ and $varepsilon_G(v)$ is the eccentricity of $v$. In this paper, we characterize the unique trees with the maximum and minimum CEI among all $n$-vertex trees and $n$-vertex conjugated trees with fixed maximum degree, respectively.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"10 1","pages":"239-246"},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208802","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 Varchenko determinant of an oriented matroid 有向矩阵的瓦琴科行列式
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-01 DOI: 10.22108/TOC.2021.125990.1780
H. Randriamaro
{"title":"The Varchenko determinant of an oriented matroid","authors":"H. Randriamaro","doi":"10.22108/TOC.2021.125990.1780","DOIUrl":"https://doi.org/10.22108/TOC.2021.125990.1780","url":null,"abstract":"Varchenko introduced in 1993 a distance function on the chambers of a hyperplane arrangement that gave rise to a determinant whose entry in position $(C, D)$ is the distance between the chambers $C$ and $D$, and computed that determinant. In 2017, Aguiar and Mahajan provided a generalization of that distance function, and computed the corresponding determinant. This article extends their distance function to the topes of an oriented matroid, and computes the determinant thus defined. Oriented matroids have the nice property to be abstractions of some mathematical structures including hyperplane and sphere arrangements, polytopes, directed graphs, and even chirality in molecular chemistry. Independently and with another method, Hochst\"{a}ttler and Welker also computed in 2019 the same determinant.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"10 1","pages":"213-224"},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208819","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
Forcing edge detour monophonic number of a graph 图的强制边绕道单音数
IF 0.4
Transactions on Combinatorics Pub Date : 2021-01-01 DOI: 10.22108/TOC.2021.119182.1670
P. Titus, K. Ganesamoorthy
{"title":"Forcing edge detour monophonic number of a graph","authors":"P. Titus, K. Ganesamoorthy","doi":"10.22108/TOC.2021.119182.1670","DOIUrl":"https://doi.org/10.22108/TOC.2021.119182.1670","url":null,"abstract":"‎For a connected graph $G=(V,E)$ of order at least two‎, ‎an edge detour monophonic set of $G$ is a set $S$ of vertices such that every edge of $G$ lies on a detour monophonic path joining some pair of vertices in $S$‎. ‎The edge detour monophonic number of $G$ is the minimum cardinality of its edge detour monophonic sets and is denoted by $edm(G)$‎. ‎A subset $T$ of $S$ is a forcing edge detour monophonic subset for $S$ if $S$ is the unique edge detour monophonic set of size $edm(G)$ containing $T$‎. ‎A forcing edge detour monophonic subset for $S$ of minimum cardinality is a minimum forcing edge detour monophonic subset of $S$‎. ‎The forcing edge detour monophonic number $f_{edm}(S)$ in $G$ is the cardinality of a minimum forcing edge detour monophonic subset of $S$‎. ‎The forcing edge detour monophonic number of $G$ is $f_{edm}(G)=min{f_{edm}(S)}$‎, ‎where the minimum is taken over all edge detour monophonic sets $S$ of size $edm(G)$ in $G$‎. ‎We determine bounds for it and find the forcing edge detour monophonic number of certain classes of graphs‎. ‎It is shown that for every pair a‎, ‎b of positive integers with $0leq a","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"66 1","pages":"201-211"},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68208755","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
Gutman index, edge-Wiener index and edge-connectivity Gutman指数、边- wiener指数和边-连通性
IF 0.4
Transactions on Combinatorics Pub Date : 2020-12-01 DOI: 10.22108/TOC.2020.124104.1749
J. P. Mazorodze, S. Mukwembi, T. Vetrík
{"title":"Gutman index, edge-Wiener index and edge-connectivity","authors":"J. P. Mazorodze, S. Mukwembi, T. Vetrík","doi":"10.22108/TOC.2020.124104.1749","DOIUrl":"https://doi.org/10.22108/TOC.2020.124104.1749","url":null,"abstract":"‎We study the Gutman index ${rm Gut}(G)$ and the edge-Wiener index $W_e (G)$ of connected graphs $G$ of given order $n$ and edge-connectivity $lambda$‎. ‎We show that the bound ${rm Gut}(G) le frac{2^4 cdot 3}{5^5 (lambda+1)} n^5‎ + ‎O(n^4)$ is asymptotically tight for $lambda ge 8$‎. ‎We improve this result considerably for $lambda le 7$ by presenting asymptotically tight upper bounds on ${rm Gut}(G)$ and $W_e (G)$ for $2 le lambda le 7$‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"9 1","pages":"231-242"},"PeriodicalIF":0.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47887082","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
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