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On generalized strong complete mappings and mutually orthogonal Latin squares 关于广义强完备映射和相互正交的拉丁平方
Ars Math. Contemp. Pub Date : 2021-04-14 DOI: 10.26493/1855-3974.2388.928
A. Muratovic-Ribic
{"title":"On generalized strong complete mappings and mutually orthogonal Latin squares","authors":"A. Muratovic-Ribic","doi":"10.26493/1855-3974.2388.928","DOIUrl":"https://doi.org/10.26493/1855-3974.2388.928","url":null,"abstract":"We present an application of generalized strong complete mappings to construction of a family of mutually orthogonal Latin squares. We also determine a cycle structure of such mapping which form a complete family of MOLS. Many constructions of generalized strong complete mappings over an extension of finite field are provided.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89191883","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
Modifications of the Floyd-Warshall algorithm with nearly quadratic expected-time 近似二次期望时间Floyd-Warshall算法的改进
Ars Math. Contemp. Pub Date : 2021-04-13 DOI: 10.26493/1855-3974.2467.497
A. Brodnik, Marko Grgurovic, Rok Požar
{"title":"Modifications of the Floyd-Warshall algorithm with nearly quadratic expected-time","authors":"A. Brodnik, Marko Grgurovic, Rok Požar","doi":"10.26493/1855-3974.2467.497","DOIUrl":"https://doi.org/10.26493/1855-3974.2467.497","url":null,"abstract":"The paper describes two relatively simple modifications of the well-known FloydWarshall algorithm for computing all-pairs shortest paths. A fundamental difference of both modifications in comparison to the Floyd-Warshall algorithm is that the relaxation is done in a smart way. We show that the expected-case time complexity of both algorithms is O(n log n) for the class of complete directed graphs on n vertices with arc weights selected independently at random from the uniform distribution on [0, 1]. Theoretically best known algorithms for this class of graphs are all based on Dijkstra’s algorithm and obtain a better expected-case bound. However, by conducting an empirical evaluation we prove that our algorithms are at least competitive in practice with best know algorithms and, moreover, outperform most of them. The reason for the practical efficiency of the presented algorithms is the absence of use of priority queue. ∗A preliminary version of this work has been published in Shortest Path Solvers: From Software to Wetware, volume 32 of Emergence, Complexity and Computation (2018). The authors would like to thank the reviewer for excellent comments that substantially improved the quality of the paper. †This work is sponsored in part by the Slovenian Research Agency (research program P2-0359 and research projects J1-2481, J2-2504, and N2-0171). ‡Corresponding author. This work is supported in part by the Slovenian Research Agency (research program P1-0285 and research projects N1-0062, J1-9110, J1-9187, J1-1694, N1-0159, J1-2451). cb This work is licensed under https://creativecommons.org/licenses/by/4.0/ Ac ce pt ed m an us cr ip t 2 Ars Math. Contemp.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"26 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73707447","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
Nonlinear maps preserving the elementary symmetric functions 保持初等对称函数的非线性映射
Ars Math. Contemp. Pub Date : 2021-04-11 DOI: 10.26493/1855-3974.2488.F5C
C. Costara
{"title":"Nonlinear maps preserving the elementary symmetric functions","authors":"C. Costara","doi":"10.26493/1855-3974.2488.F5C","DOIUrl":"https://doi.org/10.26493/1855-3974.2488.F5C","url":null,"abstract":"","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"77 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83977158","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
Enumerating symmetric peaks in non-decreasing Dyck paths 枚举非递减戴克路径中的对称峰
Ars Math. Contemp. Pub Date : 2021-04-11 DOI: 10.26493/1855-3974.2478.D1B
S. Elizalde, Rigoberto Flórez, J. L. Ramírez
{"title":"Enumerating symmetric peaks in non-decreasing Dyck paths","authors":"S. Elizalde, Rigoberto Flórez, J. L. Ramírez","doi":"10.26493/1855-3974.2478.D1B","DOIUrl":"https://doi.org/10.26493/1855-3974.2478.D1B","url":null,"abstract":"","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87097089","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
A note on the k-tuple domination number of graphs 关于图的k元组支配数的注意事项
Ars Math. Contemp. Pub Date : 2021-04-07 DOI: 10.26493/1855-3974.2600.dcc
Abel Cabrera Martínez
{"title":"A note on the k-tuple domination number of graphs","authors":"Abel Cabrera Martínez","doi":"10.26493/1855-3974.2600.dcc","DOIUrl":"https://doi.org/10.26493/1855-3974.2600.dcc","url":null,"abstract":"In a graph G, a vertex dominates itself and its neighbours. A set D ⊆ V (G) is said to be a k-tuple dominating set of G if D dominates every vertex of G at least k times. The minimum cardinality among all k-tuple dominating sets is the k-tuple domination number of G. In this note, we provide new bounds on this parameter. Some of these bounds generalize other ones that have been given for the case k = 2.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"8 1","pages":"4"},"PeriodicalIF":0.0,"publicationDate":"2021-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74086572","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
A family of fractal non-contracting weakly branch groups 一类分形非收缩弱支群
Ars Math. Contemp. Pub Date : 2021-04-06 DOI: 10.26493/1855-3974.2338.5DF
M. Noce
{"title":"A family of fractal non-contracting weakly branch groups","authors":"M. Noce","doi":"10.26493/1855-3974.2338.5DF","DOIUrl":"https://doi.org/10.26493/1855-3974.2338.5DF","url":null,"abstract":"We construct a new example of an infinite family of groups acting on a d -adic tree, with d  ≥ 2 that is non-contracting and weakly regular branch over the derived subgroup.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"44 1","pages":"29-36"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87550330","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
Wiener-type indices of Parikh word representable graphs Parikh词可表示图的wiener型索引
Ars Math. Contemp. Pub Date : 2021-03-12 DOI: 10.26493/1855-3974.2359.A7B
Nobin Thomas, Lisa Mathew, S. Sriram, K. Subramanian
{"title":"Wiener-type indices of Parikh word representable graphs","authors":"Nobin Thomas, Lisa Mathew, S. Sriram, K. Subramanian","doi":"10.26493/1855-3974.2359.A7B","DOIUrl":"https://doi.org/10.26493/1855-3974.2359.A7B","url":null,"abstract":"A new class of graphs G(w), called  Parikh word representable graphs (PWRG), corresponding to words $w$ that are finite sequence of symbols, was considered in the recent past. Several properties of these graphs have been established. In this paper, we consider these graphs corresponding to binary core words of the form $aub$ over a binary alphabet {a,b}.  We derive formulas for computing the Wiener index of the PWRG of a binary core word. Sharp bounds are established on the value of this index in terms of different parameters related to binary words over {a,b} and the corresponding PWRGs. Certain other Wiener-type indices that are variants of Wiener index are also considered. Formulas for computing these indices in the case of PWRG of a binary core word are obtained.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"51 1","pages":"243-260"},"PeriodicalIF":0.0,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79541992","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
Geometry of the parallelism in polar spine spaces and their line reducts 几何平行的极脊空间和他们的线减少
Ars Math. Contemp. Pub Date : 2021-03-11 DOI: 10.26493/1855-3974.2201.B65
K. Petelczyc, K. Prażmowski, M. Żynel
{"title":"Geometry of the parallelism in polar spine spaces and their line reducts","authors":"K. Petelczyc, K. Prażmowski, M. Żynel","doi":"10.26493/1855-3974.2201.B65","DOIUrl":"https://doi.org/10.26493/1855-3974.2201.B65","url":null,"abstract":"The concept of spine geometry over a polar Grassmann space was introduced in [9]. The geometry in question belongs also to a wide family of partial affine line spaces. It is known that such a geometry -- e.g. the ``ordinary'' spine geometry, as considered in [13, 14] can be developed in terms of points, so called affine lines, and their parallelism (in this case this parallelism is not intrinsically definable: it is not `Veblenian', cf. [11]). This paper aims to prove an analogous result for polar spine spaces. As a by-product we  obtain several other results on primitive notions for the geometry of polar spine spaces.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"39 1","pages":"151-170"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77397341","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
Closed formulas for the total Roman domination number of lexicographic product graphs 字典积图的罗马统治总数的封闭公式
Ars Math. Contemp. Pub Date : 2021-03-11 DOI: 10.26493/1855-3974.2284.AEB
Abel Cabrera Martínez, J. A. Rodríguez-Velázquez
{"title":"Closed formulas for the total Roman domination number of lexicographic product graphs","authors":"Abel Cabrera Martínez, J. A. Rodríguez-Velázquez","doi":"10.26493/1855-3974.2284.AEB","DOIUrl":"https://doi.org/10.26493/1855-3974.2284.AEB","url":null,"abstract":"Let G be a graph with no isolated vertex and f :  V ( G ) → {0, 1, 2} a function. Let V i  = { x  ∈  V ( G ) : f ( x ) = i } for every i  ∈ {0, 1, 2} . We say that f is a total Roman dominating function on G if every vertex in V 0 is adjacent to at least one vertex in V 2 and the subgraph induced by V 1  ∪  V 2 has no isolated vertex. The weight of f is ω ( f ) = ∑ v  ∈  V ( G ) f ( v ) . The minimum weight among all total Roman dominating functions on G is the total Roman domination number of G , denoted by γ t R ( G ) . It is known that the general problem of computing γ t R ( G ) is NP-hard. In this paper, we show that if G is a graph with no isolated vertex and H is a nontrivial graph, then the total Roman domination number of the lexicographic product graph G  ∘  H is given by γ t R ( G  ∘  H ) = 2 γ t ( G ) if γ ( H ) ≥ 2, and γ t R ( G  ∘  H ) = ξ ( G ) if γ ( H ) = 1 , where γ ( H ) is the domination number of H , γ t ( G ) is the total domination number of G and ξ ( G ) is a domination parameter defined on G .","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"52 1","pages":"233-241"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75954729","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: 8
Nordhaus-Gaddum type inequalities for the distinguishing index 区分指标的Nordhaus-Gaddum型不等式
Ars Math. Contemp. Pub Date : 2021-03-04 DOI: 10.26493/1855-3974.2173.71A
M. Pilsniak
{"title":"Nordhaus-Gaddum type inequalities for the distinguishing index","authors":"M. Pilsniak","doi":"10.26493/1855-3974.2173.71A","DOIUrl":"https://doi.org/10.26493/1855-3974.2173.71A","url":null,"abstract":"The distinguishing index of a graph G, denoted by D′(G), is the least number of colours in an edge colouring of G not preserved by any nontrivial automorphism. This invariant is defined for any graph without K2 as a connected component and without two isolated vertices, and such a graph is called admissible. We prove the Nordhaus-Gaddum type relation: 2 ≤ D′(G) +D′(G) ≤ ∆(G) + 2 for every admissible connected graph G of order |G| ≥ 7 such that G is also admissible.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"142 1","pages":"223-231"},"PeriodicalIF":0.0,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87965385","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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