Pub Date : 2023-04-03DOI: 10.26493/1855-3974.3061.5bf
Rigoberto Flórez, J. L. Ramírez
{"title":"Enumerating symmetric pyramids in Motzkin paths","authors":"Rigoberto Flórez, J. L. Ramírez","doi":"10.26493/1855-3974.3061.5bf","DOIUrl":"https://doi.org/10.26493/1855-3974.3061.5bf","url":null,"abstract":"","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83211452","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}
Pub Date : 2023-01-13DOI: 10.26493/1855-3974.2683.5f3
S. H. Alavi, A. Daneshkhah, Fatemeh Mouseli
{"title":"Almost simple groups as flag-transitive automorphism groups of symmetric designs with λ prime","authors":"S. H. Alavi, A. Daneshkhah, Fatemeh Mouseli","doi":"10.26493/1855-3974.2683.5f3","DOIUrl":"https://doi.org/10.26493/1855-3974.2683.5f3","url":null,"abstract":"","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80847631","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}
Pub Date : 2022-10-05DOI: 10.26493/1855-3974.2707.29c
A. Caggegi
In this paper we construct a family of 2 - ( q n , sp 2 , λ ) additive designs D = ( P , B ) , where q is a power of a prime p and P is a n -dimensional vector space over GF( q ) and we compute their parameters explicitly. These designs, except for some special cases, had not been considered in the previous literature on additive block designs.
本文构造了一类2 - (q n, sp 2， λ)可加设计D = (P, B)，其中q是素数P的幂，P是GF(q)上的n维向量空间，并显式地计算了它们的参数。这些设计，除了一些特殊情况，没有考虑在以前的文献中添加块设计。
{"title":"A new family of additive designs","authors":"A. Caggegi","doi":"10.26493/1855-3974.2707.29c","DOIUrl":"https://doi.org/10.26493/1855-3974.2707.29c","url":null,"abstract":"In this paper we construct a family of 2 - ( q n , sp 2 , λ ) additive designs D = ( P , B ) , where q is a power of a prime p and P is a n -dimensional vector space over GF( q ) and we compute their parameters explicitly. These designs, except for some special cases, had not been considered in the previous literature on additive block designs.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75974576","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}
Pub Date : 2022-08-18DOI: 10.26493/1855-3974.2697.43a
A. Alhevaz, M. Baghipur, H. A. Ganie, K. Das
For a simple graph G , the generalized adjacency matrix A α ( G ) is defined as A α ( G ) = αD ( G ) + (1 − α ) A ( G ) , α ∈ [0 , 1] , where A ( G ) is the adjacency matrix and D ( G ) is the diagonal matrix of the vertex degrees. It is clear that A 0 ( G ) = A ( G ) and 2 A 12 ( G ) = Q ( G ) implying that the matrix A α ( G ) is a generalization of the adjacency matrix and the signless Laplacian matrix. In this paper, we obtain some new upper and lower bounds for the generalized adjacency spectral radius λ ( A α ( G )) , in terms of vertex degrees, average vertex 2 -degrees, the order, the size, etc. The extremal graphs attaining these bounds are characterized. We will show that our bounds are better than some of the already known bounds for some classes of graphs. We derive a general upper bound for λ ( A α ( G )) , in terms of vertex degrees and positive real numbers b i . As application, we obtain some new upper bounds for λ ( A α ( G )) . Further, we obtain some relations between clique number ω ( G ) , independence number γ ( G ) and the generalized adjacency eigenvalues of a graph G .
对于简单图G，定义广义邻接矩阵a α (G)为a α (G) = αD (G) +(1−α) a (G)， α∈[0,1]，其中a (G)为邻接矩阵，D (G)为顶点度的对角矩阵。很明显，a0 (G) = A (G)和2a12 (G) = Q (G)，这意味着矩阵A α (G)是邻接矩阵和无符号拉普拉斯矩阵的推广。本文给出了广义邻接谱半径λ (A α (G))在顶点度、平均顶点2度、阶数、大小等方面的上界和下界。对达到这些边界的极值图进行了表征。我们将证明，对于某些类型的图，我们的界比一些已知的界要好。我们导出了λ (a α (G))的一般上界，用顶点度数和正实数bi表示。作为应用，得到了λ (A α (G))的一些新的上界。进一步，我们得到了图G的团数ω (G)、独立数γ (G)与广义邻接特征值之间的关系。
{"title":"On the Aα-spectral radius of connected graphs","authors":"A. Alhevaz, M. Baghipur, H. A. Ganie, K. Das","doi":"10.26493/1855-3974.2697.43a","DOIUrl":"https://doi.org/10.26493/1855-3974.2697.43a","url":null,"abstract":"For a simple graph G , the generalized adjacency matrix A α ( G ) is defined as A α ( G ) = αD ( G ) + (1 − α ) A ( G ) , α ∈ [0 , 1] , where A ( G ) is the adjacency matrix and D ( G ) is the diagonal matrix of the vertex degrees. It is clear that A 0 ( G ) = A ( G ) and 2 A 12 ( G ) = Q ( G ) implying that the matrix A α ( G ) is a generalization of the adjacency matrix and the signless Laplacian matrix. In this paper, we obtain some new upper and lower bounds for the generalized adjacency spectral radius λ ( A α ( G )) , in terms of vertex degrees, average vertex 2 -degrees, the order, the size, etc. The extremal graphs attaining these bounds are characterized. We will show that our bounds are better than some of the already known bounds for some classes of graphs. We derive a general upper bound for λ ( A α ( G )) , in terms of vertex degrees and positive real numbers b i . As application, we obtain some new upper bounds for λ ( A α ( G )) . Further, we obtain some relations between clique number ω ( G ) , independence number γ ( G ) and the generalized adjacency eigenvalues of a graph G .","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89742492","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}
Pub Date : 2022-07-29DOI: 10.26493/1855-3974.2706.3c8
Xin He, Heping Zhang
The complete forcing number of a graph G with a perfect matching is the minimum cardinality of an edge set of G on which the restriction of each perfect matching M is a forcing set of M . This concept can be view as a strengthening of the concept of global forcing number of G . Do ˇ sli ´ c (2007) obtained that the global forcing number of a connected graph is at most its cyclomatic number. Motivated from this result, we obtain that the complete forcing number of a graph is no more than 2 times its cyclomatic number and characterize the matching covered graphs whose complete forcing numbers attain this upper bound and minus one, respectively. Besides, we present a method of constructing a complete forcing set of a graph. By using such method, we give closed formulas for the complete forcing numbers of wheels and cylinders.
{"title":"Complete forcing numbers of graphs","authors":"Xin He, Heping Zhang","doi":"10.26493/1855-3974.2706.3c8","DOIUrl":"https://doi.org/10.26493/1855-3974.2706.3c8","url":null,"abstract":"The complete forcing number of a graph G with a perfect matching is the minimum cardinality of an edge set of G on which the restriction of each perfect matching M is a forcing set of M . This concept can be view as a strengthening of the concept of global forcing number of G . Do ˇ sli ´ c (2007) obtained that the global forcing number of a connected graph is at most its cyclomatic number. Motivated from this result, we obtain that the complete forcing number of a graph is no more than 2 times its cyclomatic number and characterize the matching covered graphs whose complete forcing numbers attain this upper bound and minus one, respectively. Besides, we present a method of constructing a complete forcing set of a graph. By using such method, we give closed formulas for the complete forcing numbers of wheels and cylinders.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"186 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83044979","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}
Pub Date : 2022-06-06DOI: 10.26493/1855-3974.2507.a1d
Eugenia O'Reilly Regueiro, José Emanuel Rodríguez-Fitta
We study (v, k, λ)-symmetric designs having a flag-transitive, point-primitive automorphism group, with v = m and (k, λ) = t > 1, and prove that if D is such a design with m even admitting a flag-transitive, point-primitive automorphism group G, then either: (1) D is a design with parameters ( (2t+ s− 1), 2t −(2−s)t s , t−t s2 ) with s ≥ 1 odd, or (2) G does not have a non-trivial product action. We observe that the parameters in (1), when s = 1, correspond to Menon designs. We also prove that if D is a (v, k, λ)-symmetric design with a flag-transitive, pointprimitive automorphism group of product action type with v = m and l ≥ 2 then the complement of D does not admit a flag-transitive automorphism group.
我们研究(v, k,λ)对称设计flag-transitive, point-primitive自同构群,与v = m和(k,λ)= t > 1,证明如果D是这样的设计和m甚至承认flag-transitive point-primitive自同构群G,然后要么:(1)D是一个设计参数((2 t + s−1),2 t−(2−(s) t s、t−s2)和s≥1奇怪,或(2)G产品没有一个非平凡的行动。我们观察到，当s = 1时，(1)中的参数对应于Menon设计。我们还证明了如果D是一个(v, k， λ)-对称设计，具有v = m且l≥2的积作用型标志-传递点基自同构群，则D的补不存在标志-传递自同构群。
{"title":"A parametrisation for symmetric designs admitting a flag-transitive, point-primitive automorphism group with a product action","authors":"Eugenia O'Reilly Regueiro, José Emanuel Rodríguez-Fitta","doi":"10.26493/1855-3974.2507.a1d","DOIUrl":"https://doi.org/10.26493/1855-3974.2507.a1d","url":null,"abstract":"We study (v, k, λ)-symmetric designs having a flag-transitive, point-primitive automorphism group, with v = m and (k, λ) = t > 1, and prove that if D is such a design with m even admitting a flag-transitive, point-primitive automorphism group G, then either: (1) D is a design with parameters ( (2t+ s− 1), 2t −(2−s)t s , t−t s2 ) with s ≥ 1 odd, or (2) G does not have a non-trivial product action. We observe that the parameters in (1), when s = 1, correspond to Menon designs. We also prove that if D is a (v, k, λ)-symmetric design with a flag-transitive, pointprimitive automorphism group of product action type with v = m and l ≥ 2 then the complement of D does not admit a flag-transitive automorphism group.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88339828","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}
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