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Variations on the Missionaries and Cannibals Problem 传教士与食人族问题的变化
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-10-21 DOI: 10.47443/dml.2022.186
G. Spahn, D. Zeilberger
{"title":"Variations on the Missionaries and Cannibals Problem","authors":"G. Spahn, D. Zeilberger","doi":"10.47443/dml.2022.186","DOIUrl":"https://doi.org/10.47443/dml.2022.186","url":null,"abstract":"We explore both automated and human approaches to the generalized Missionaries and Cannibals problem.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42987171","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 Comaximal (Ideal) Graph Associated With Amalgamated Algebra 关于合并代数的最大(理想)图
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-10-05 DOI: 10.47443/dml.2022.095
Zinat Rastgar, K. Khashyarmanesh, M. Afkhami
{"title":"On the Comaximal (Ideal) Graph Associated With Amalgamated Algebra","authors":"Zinat Rastgar, K. Khashyarmanesh, M. Afkhami","doi":"10.47443/dml.2022.095","DOIUrl":"https://doi.org/10.47443/dml.2022.095","url":null,"abstract":"Let f : A → B be a ring homomorphism of the commutative rings A and B with identities. Let J be an ideal of B . The amalgamation of A with B along J with respect to f is a subring of A × B given by A (cid:46)(cid:47) f J := { ( a, f ( a )+ j ) | a ∈ A , j ∈ J } . In this paper, we investigate the comaximal ideal graph and the comaximal graph of the amalgamated algebra A (cid:46)(cid:47) f J . In particular, we determine the Jacobson radical of A (cid:46)(cid:47) f J , characterize the diameter of the comaximal ideal graph of A (cid:46)(cid:47) f J , and investigate the clique number as well as the chromatic number of this graph.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45130722","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
Irregular Domination Trees and Forests 不规则统治树和森林
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-09-28 DOI: 10.47443/dml.2022.119
Caryn Mays, Ping Zhang
{"title":"Irregular Domination Trees and Forests","authors":"Caryn Mays, Ping Zhang","doi":"10.47443/dml.2022.119","DOIUrl":"https://doi.org/10.47443/dml.2022.119","url":null,"abstract":"A set S of vertices in a connected graph G is an irregular dominating set if the vertices of S can be labeled with distinct positive integers in such a way that for every vertex v of G , there is a vertex u ∈ S such that the distance from u to v is the label assigned to u . If for every vertex u ∈ S , there is a vertex v of G such that u is the only vertex of S whose distance to v is the label of u , then S is a minimal irregular dominating set. A graph H is an irregular domination graph if there exists a graph G with a minimal irregular dominating set S such that H is isomorphic to the subgraph G [ S ] of G induced by S . In this paper, all irregular domination trees and forests are characterized. All disconnected irregular domination graphs are determined as well.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43347341","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 Disjoint Cross Intersecting Families of Permutations 关于不相交的交叉排列族
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-09-21 DOI: 10.47443/dml.2022.110
Nuttanon Songsuwan, Supida Sengsamak, Nutchapol Jeerawattana, T. Jiarasuksakun, P. Kaemawichanurat
{"title":"On Disjoint Cross Intersecting Families of Permutations","authors":"Nuttanon Songsuwan, Supida Sengsamak, Nutchapol Jeerawattana, T. Jiarasuksakun, P. Kaemawichanurat","doi":"10.47443/dml.2022.110","DOIUrl":"https://doi.org/10.47443/dml.2022.110","url":null,"abstract":"For the positive integers r and n satisfying r ≤ n , let P r,n be the family of partial permutations {{ (1 , x 1 ) , (2 , x 2 ) , . . . , ( r, x r ) } : x 1 , x 2 , . . . , x r are different elements of { 1 , 2 , . . . , n }} . The subfamilies A 1 , A 2 , . . . , A k of P r,n are called cross intersecting if A ∩ B (cid:54) = ∅ for all A ∈ A i and B ∈ A j , where 1 ≤ i (cid:54) = j ≤ k . Also, if A 1 , A 2 , . . . , A k are mutually disjoint, then they are called disjoint cross intersecting subfamilies of P r,n . For the disjoint cross intersecting subfamilies A 1 , A 2 , . . . , A k of P n,n , it follows from the AM-GM inequality that (cid:81) ki =1 |A i | ≤ ( n ! /k ) k . In this paper, we present two proofs of the following statement: (cid:81) ki =1 |A i | = ( n ! /k ) k if and only if n = 3 and k = 2 . permutations; intersecting families; Erd˝os-Ko-Rado Theorem.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45509517","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
Computing the Sum of k Largest Laplacian Eigenvalues of Tricyclic Graphs 计算三环图的k个最大拉普拉斯特征值和
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-09-20 DOI: 10.47443/dml.2022.085
Pawan Kumar, S. Merajuddin, S. Pirzada
{"title":"Computing the Sum of k Largest Laplacian Eigenvalues of Tricyclic Graphs","authors":"Pawan Kumar, S. Merajuddin, S. Pirzada","doi":"10.47443/dml.2022.085","DOIUrl":"https://doi.org/10.47443/dml.2022.085","url":null,"abstract":"Let G ( V, E ) be a simple graph with | V ( G ) | = n and | E ( G ) | = m . If S k ( G ) is the sum of k largest Laplacian eigenvalues of G , then Brouwer’s conjecture states that S k ( G ) ≤ m + k ( k +1)2 for 1 ≤ k ≤ n . The girth of a graph G is the length of a smallest cycle in G . If g is the girth of G , then we show that the mentioned conjecture is true for 1 ≤ k ≤ (cid:98) g − 22 (cid:99) . Wang et al. [ Math. Comput. Model. 56 (2012) 60–68] proved that Brouwer’s conjecture is true for bicyclic and tricyclic graphs whenever 1 ≤ k ≤ n with k (cid:54) = 3 . We settle the conjecture under discussion also for tricyclic graphs having no pendant vertices when k = 3 .","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43979861","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 Degree-Based Topological Indices and (Normalized Laplacian) Energy of Graphs 图的一些基于度的拓扑指标和归一化拉普拉斯能量
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-09-20 DOI: 10.47443/dml.2022.059
Zimo Yan, Xie Zheng, Jianping Li
{"title":"Some Degree-Based Topological Indices and (Normalized Laplacian) Energy of Graphs","authors":"Zimo Yan, Xie Zheng, Jianping Li","doi":"10.47443/dml.2022.059","DOIUrl":"https://doi.org/10.47443/dml.2022.059","url":null,"abstract":"In this paper, by utilizing the concept of the energy of a vertex, connections between some vertex-degree-based topological indices (including the general Randi´c index, the first Zagreb index, and the forgotten index) and the energy of graphs are established. Several bounds on the energy of the graphs containing no isolated vertices are also given in terms of the first Zagreb index and the forgotten index. Moreover, bounds on the normalized Laplacian energy in terms of two particular cases of the general Randi´c index are obtained.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41492917","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 Last New Vertex Visited by a Random Walk in a Directed Graph 关于有向图随机漫步最后访问的新顶点
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-09-16 DOI: 10.47443/dml.2022.158
Calum Buchanan, P. Horn, Puck Rombach
{"title":"On the Last New Vertex Visited by a Random Walk in a Directed Graph","authors":"Calum Buchanan, P. Horn, Puck Rombach","doi":"10.47443/dml.2022.158","DOIUrl":"https://doi.org/10.47443/dml.2022.158","url":null,"abstract":"Consider a simple graph in which a random walk begins at a given vertex. It moves at each step with equal probability to any neighbor of its current vertex, and ends when it has visited every vertex. We call such a random walk a random cover tour. It is well known that cycles and complete graphs have the property that a random cover tour starting at any vertex is equally likely to end at any other vertex. Ronald Graham asked whether there are any other graphs with this property. In 1993, L'aszlo Lov'asz and Peter Winkler showed that cycles and complete graphs are the only undirected graphs with this property. We strengthen this result by showing that cycles and complete graphs (with all edges considered bidirected) are the only directed graphs with this property.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46068065","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
Applications of Zeilberger’s Algorithm to Ramanujan-Inspired Series Involving Harmonic-Type Numbers Zeilberger算法在涉及谐波型数的ramanujan启发级数中的应用
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-09-10 DOI: 10.47443/dml.2022.050
J. Campbell
{"title":"Applications of Zeilberger’s Algorithm to Ramanujan-Inspired Series Involving Harmonic-Type Numbers","authors":"J. Campbell","doi":"10.47443/dml.2022.050","DOIUrl":"https://doi.org/10.47443/dml.2022.050","url":null,"abstract":"A “harmonic variant” of Zeilberger’s algorithm is utilized to improve upon the results introduced by Wang and Chu [ Ramanujan J. 52 (2020) 641–668]. Wang and Chu’s coefficient-extraction methodologies yielded evaluations for Ramanujan-like series involving summand factors of the form H 3 n +3 H n H (2) n +2 H (3) n , where H n denotes a harmonic number and H ( x ) n is a generalized harmonic number. However, it is unclear as to how Wang and Chu’s techniques could be applied to improve upon such results by separately evaluating the series obtained upon the expansion of the summands according to the terms of the factor H 3 n +3 H n H (2) n +2 H (3) n . In this note, we succeed in applying Zeilberger’s algorithm toward this problem, providing explicit evaluations for the series with a factor of the form H (3) n obtained from the aforementioned expansion. Our approach toward generalizing Zeilberger’s algorithm to non-hypergeometric expressions may be applied much more broadly. The series obtained by replacing H (3) n with H (2) n were highlighted as especially beautiful motivating examples in Wang and Chu’s article. These H (2) n -series motivate our main results, which are natural higher-order extensions of these H (2) n -series.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47714167","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
An Interview With Ortrud Oellermann 专访奥特鲁德·奥勒曼
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-09-02 DOI: 10.47443/dml.2022.i1
Akbar Ali
{"title":"An Interview With Ortrud Oellermann","authors":"Akbar Ali","doi":"10.47443/dml.2022.i1","DOIUrl":"https://doi.org/10.47443/dml.2022.i1","url":null,"abstract":"Ortrud R. Oellermann received an M.Sc. in mathematics from the University of Natal, South Africa in 1983 and a Ph.D. in mathematics from Western Michigan University, USA in 1986. She taught at several universities, but the majority of her academic career was spent at the University of Winnipeg, Canada, where she served from July 1996 until August 31, 2021, when she retired as a professor. She is currently an adjunct professor of mathematics at both the University of Winnipeg and the University of Victoria, Canada. Professor Oellermann was honoured with a Professor Emerita title from the University of Winnipeg in June 2022. Throughout her career she held research grant funding from research funding agencies such as the Office of Naval Research (USA), the National Research Foundation (South Africa) and NSERC (Canada). To date she has 85 co-authors of which 22 are former research students or post-doctoral fellows. She is currently one of four editors-in-chief of the Bulletin of the Institute of Combinatorics and its Applications. Previously she served on the editorial boards of Ars Combinatoria and Utilitas Mathematics. Professor Oellermann has received several medals, including the Hall Medal from the Institute of Combinatorics and its Applications in 1995. She was an elected member of the board of directors of the Canadian Mathematical Society (July 2001 June 2005) and the executive committee of the Discrete Mathematics activity group of the Society for Industrial and Applied Mathematics (January 2006 December 2007). Professor Oellermann also served as an academic consultant for the Cambridge University Press monograph “Topics in Structural Graph Theory” edited by Lowell W. Beineke and Robin J. Wilson.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42144537","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 New Proof of Boole’S Additive Combinatorics Formula 布尔加法组合数学公式的一个新证明
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-09-02 DOI: 10.47443/dml.2022.109
Necdet Batır, S. Atpinar
{"title":"A New Proof of Boole’S Additive Combinatorics Formula","authors":"Necdet Batır, S. Atpinar","doi":"10.47443/dml.2022.109","DOIUrl":"https://doi.org/10.47443/dml.2022.109","url":null,"abstract":"The Boole’s additive combinatorics formula is given by n (cid:88) k =0 ( − 1) n − k (cid:32) n k (cid:33) k m =   0 if m < n, n ! if m = n. A new proof of this formula is presented in this paper.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46250372","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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