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Art of Discrete and Applied Mathematics最新文献

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The length of the initial longest increasing sequence in a permutation 排列中初始最长递增序列的长度
Art of Discrete and Applied Mathematics Pub Date : 2023-01-04 DOI: 10.26493/2590-9770.1516.96f
T. Mansour
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引用次数: 0
Disconnected spanning subgraphs of paths in the join products with cycles 在带有循环的连接乘积中，路径的断开的生成子图
Art of Discrete and Applied Mathematics Pub Date : 2022-12-22 DOI: 10.26493/2590-9770.1540.7b1
M. Staš, M. Švecová
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引用次数: 0
Asymmetrizing cost and density of vertex-transitive cubic graphs 顶点传递三次图的非对称代价和密度
Art of Discrete and Applied Mathematics Pub Date : 2022-08-24 DOI: 10.26493/2590-9770.1395.a37
W. Imrich, T. Lachmann, T. Tucker, G. Wiegel
{"title":"Asymmetrizing cost and density of vertex-transitive cubic graphs","authors":"W. Imrich, T. Lachmann, T. Tucker, G. Wiegel","doi":"10.26493/2590-9770.1395.a37","DOIUrl":"https://doi.org/10.26493/2590-9770.1395.a37","url":null,"abstract":"A set S of vertices in a graph G with nontrivial automorphism group is asymmetrizing if the identity mapping is the only automorphism of G that preserves S as a set. If such sets exist, then their minimum cardinality is the asymmetrizing cost ρ ( G ) of G . For finite graphs the asymmetrizing density δ ( G ) of G is the quotient of the size of S by the order of G . For infinite graphs δ ( G ) is defined by a limit process. Many classes of infinite graphs with δ ( G ) = 0 are known, but seemingly no infinite vertex transitive graphs with δ ( G ) > 0. Here, we construct connected, infinite vertex transitive cubic graphs of asymmetrizing density δ ( G ) = 1 n 2 n +1 for each n ≥ 1. We also construct finite vertex transitive cubic graphs of arbitrarily large asymmetrizing cost. The examples are Split Praeger–Xu graphs, for which we provide another characterization. This contrasts with our results for vertex transitive cubic graphs that have one arc orbit or are so-called synchronously connected graphs with two arc orbits. For them we show that ρ ( G ) is either ≤ 5 or infinite. In the latter case δ ( G ) = 0.","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48043727","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
On the achromatic number of the Cartesian product of two complete graphs 两个完全图的笛卡儿积的消色差数
Art of Discrete and Applied Mathematics Pub Date : 2022-07-03 DOI: 10.26493/2590-9770.1555.9a6
M. Horňák
{"title":"On the achromatic number of the Cartesian product of two complete graphs","authors":"M. Horňák","doi":"10.26493/2590-9770.1555.9a6","DOIUrl":"https://doi.org/10.26493/2590-9770.1555.9a6","url":null,"abstract":"A vertex colouring $f:V(G)to C$ of a graph $G$ is complete if for any $c_1,c_2in C$ with $c_1ne c_2$ there are in $G$ adjacent vertices $v_1,v_2$ such that $f(v_1)=c_1$ and $f(v_2)=c_2$. The achromatic number of $G$ is the maximum number $mathrm{achr}(G)$ of colours in a proper complete vertex colouring of $G$. Let $G_1square G_2$ denote the Cartesian product of graphs $G_1$ and $G_2$. In the paper $mathrm{achr}(K_{r^2+r+1}square K_q)$ is determined for an infinite number of $q$s provided that $r$ is a finite projective plane order.","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":"25 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69338932","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 polynomials of small degree over finite fields representing quadratic residues 有限域上表示二次残数的小次多项式
Art of Discrete and Applied Mathematics Pub Date : 2022-06-21 DOI: 10.26493/2590-9770.1468.a2e
Shao-Fei Du, Kai Yuan
{"title":"On polynomials of small degree over finite fields representing quadratic residues","authors":"Shao-Fei Du, Kai Yuan","doi":"10.26493/2590-9770.1468.a2e","DOIUrl":"https://doi.org/10.26493/2590-9770.1468.a2e","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47893082","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
Clar and Fries structures for fullerenes 富勒烯的Clar和Fries结构
Art of Discrete and Applied Mathematics Pub Date : 2022-03-04 DOI: 10.26493/2590-9770.1510.22d
P. Fowler, Wendy J. Myrvold, Rebecca L. Vandenberg, E. Hartung, J. Graver
{"title":"Clar and Fries structures for fullerenes","authors":"P. Fowler, Wendy J. Myrvold, Rebecca L. Vandenberg, E. Hartung, J. Graver","doi":"10.26493/2590-9770.1510.22d","DOIUrl":"https://doi.org/10.26493/2590-9770.1510.22d","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42993345","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
Some properties of the factors of Fermat numbers 费马数因子的一些性质
Art of Discrete and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.26493/2590-9770.1473.ec5
Lorenzo Sauras Altuzarra
{"title":"Some properties of the factors of Fermat numbers","authors":"Lorenzo Sauras Altuzarra","doi":"10.26493/2590-9770.1473.ec5","DOIUrl":"https://doi.org/10.26493/2590-9770.1473.ec5","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":"6 1","pages":"2"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69338925","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 configurations (13_3) 配置（13_3）
Art of Discrete and Applied Mathematics Pub Date : 2021-12-04 DOI: 10.26493/2590-9770.1327.9ea
W. Kocay
{"title":"The configurations (13_3)","authors":"W. Kocay","doi":"10.26493/2590-9770.1327.9ea","DOIUrl":"https://doi.org/10.26493/2590-9770.1327.9ea","url":null,"abstract":"","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47977334","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
Three conjectures of Ostrander on digraph Laplacian eigenvectors Ostrander关于有向图拉普拉斯特征向量的三个猜想
Art of Discrete and Applied Mathematics Pub Date : 2021-07-05 DOI: 10.26493/2590-9770.1420.B57
Yaokun Wu, Da Zhao
{"title":"Three conjectures of Ostrander on digraph Laplacian eigenvectors","authors":"Yaokun Wu, Da Zhao","doi":"10.26493/2590-9770.1420.B57","DOIUrl":"https://doi.org/10.26493/2590-9770.1420.B57","url":null,"abstract":"Ostrander proposed three conjectures on the connections between topological properties of a weighted digraph and combinatorial properties of its Laplacian eigenvectors. We verify one of his conjectures, give counterexamples to the other two, and then seek for related valid connections and generalizations to Schrodinger operators on countable digraphs. We suggest the open question of deciding if the countability assumption can be dropped from our main results.","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41976090","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
Connected geometric (n_k) configurations exist for almost all n 连通几何（n_k）配置几乎存在于所有n
Art of Discrete and Applied Mathematics Pub Date : 2021-06-29 DOI: 10.26493/2590-9770.1408.f90
G. Gévay, Leah Wrenn Berman, T. Pisanski
{"title":"Connected geometric (n_k) configurations exist for almost all n","authors":"G. Gévay, Leah Wrenn Berman, T. Pisanski","doi":"10.26493/2590-9770.1408.f90","DOIUrl":"https://doi.org/10.26493/2590-9770.1408.f90","url":null,"abstract":"In a series of papers and in his 2009 book on configurations Branko Grunbaum described a sequence of operations to produce new (n4) configurations from various input configurations. These operations were later called the “Grunbaum Incidence Calculus”. We generalize two of these operations to produce operations on arbitrary (nk) configurations. Using them, we show that for any k there exists an integer Nk such that for any n ≥ Nk there exists a geometric (nk) configuration. We use empirical results for k = 2, 3, 4, and some more detailed analysis to improve the upper bound for larger values of k.","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42469045","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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