{"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}
{"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}
{"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}
{"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}
{"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}
Eugenia O'Reilly Regueiro, José Emanuel Rodríguez-Fitta
{"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}