In this manuscript, we have evaluated the energies of Smith graphs. In the course of the investigation, we found that only one Smith graph is hypo-energetic. Moreover, we have also established the energy bounds for Smith graphs.
{"title":"Energy of Smith graphs","authors":"P. Sharma, R. Naresh, U. Sharma","doi":"10.12958/ADM1071","DOIUrl":"https://doi.org/10.12958/ADM1071","url":null,"abstract":"In this manuscript, we have evaluated the energies of Smith graphs. In the course of the investigation, we found that only one Smith graph is hypo-energetic. Moreover, we have also established the energy bounds for Smith graphs.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417410","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}
Let M be the metabelian product of free abelian Lie algebras of finite rank. In this study we prove that every normal automorphism of M is an IA-automorphism and acts identically on M′.
{"title":"Normal automorphisms of the metabelian product of free abelian Lie algebras","authors":"N. Ş. Öğüşlü","doi":"10.12958/ADM1258","DOIUrl":"https://doi.org/10.12958/ADM1258","url":null,"abstract":"Let M be the metabelian product of free abelian Lie algebras of finite rank. In this study we prove that every normal automorphism of M is an IA-automorphism and acts identically on M′.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417235","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}
Special infinite families of regular graphs of unbounded degree and of bounded diameter (small world graphs) are considered. Two families of small world graphs Gi and Hi form a family of non-Sunada twins if Gi and Hi are isospectral of bounded diameter but groups Aut(Gi) and Aut(Hi) are nonisomorphic. We say that a family of non-Sunada twins is unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. If all Gi and Hi are edge-transitive we have a balanced family of small world non-Sunada twins. We say that a family of non-Sunada twins is strongly unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. We use term edge disbalanced for the family of non-Sunada twins such that all graphs Gi and Hi are edge-intransitive. We present explicit constructions of the above defined families. Two new families of distance-regular—but not distance-transitive—graphs will be introduced.
{"title":"On small world non-Sunada twins and cellular Voronoi diagrams","authors":"V. Ustimenko","doi":"10.12958/adm1343","DOIUrl":"https://doi.org/10.12958/adm1343","url":null,"abstract":"Special infinite families of regular graphs of unbounded degree and of bounded diameter (small world graphs) are considered. Two families of small world graphs Gi and Hi form a family of non-Sunada twins if Gi and Hi are isospectral of bounded diameter but groups Aut(Gi) and Aut(Hi) are nonisomorphic. We say that a family of non-Sunada twins is unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. If all Gi and Hi are edge-transitive we have a balanced family of small world non-Sunada twins. We say that a family of non-Sunada twins is strongly unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. We use term edge disbalanced for the family of non-Sunada twins such that all graphs Gi and Hi are edge-intransitive. We present explicit constructions of the above defined families. Two new families of distance-regular—but not distance-transitive—graphs will be introduced.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417433","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}
In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups Gα∪Gβ (α>β) with an injective structure homomorphism, where Gα has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case that the structure homomorphism is bijective.
{"title":"Endomorphisms of Clifford semigroups with injective structure homomorphisms","authors":"S. Worawiset, J. Koppitz","doi":"10.12958/ADM1543","DOIUrl":"https://doi.org/10.12958/ADM1543","url":null,"abstract":"In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups Gα∪Gβ (α>β) with an injective structure homomorphism, where Gα has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case that the structure homomorphism is bijective.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66418497","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}
We study an analogue of unique factorization rings in the case of an elementary divisor domain.
研究了在初等除数域上的唯一分解环的模拟。
{"title":"Comaximal factorization in a commutative Bezout ring","authors":"B. Zabavsky, O. Romaniv, B. Kuznitska, T. Hlova","doi":"10.12958/adm1203","DOIUrl":"https://doi.org/10.12958/adm1203","url":null,"abstract":"We study an analogue of unique factorization rings in the case of an elementary divisor domain.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417091","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}
Let (R,m) be a local ring, Φ a system of ideals of R and M a finitely generated R-module. In this paper, we define and study general formal local cohomology modules. We denote the ith general formal local cohomology module M with respect to Φ by FiΦ(M) and we investigate some finiteness and Artinianness properties of general formal local cohomology modules.
{"title":"General formal local cohomology modules","authors":"S. Rezaei","doi":"10.12958/ADM1068","DOIUrl":"https://doi.org/10.12958/ADM1068","url":null,"abstract":"Let (R,m) be a local ring, Φ a system of ideals of R and M a finitely generated R-module. In this paper, we define and study general formal local cohomology modules. We denote the ith general formal local cohomology module M with respect to Φ by FiΦ(M) and we investigate some finiteness and Artinianness properties of general formal local cohomology modules.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417348","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}
Let us consider W a G-set and M a Z2G-module, where G is a group. In this paper we investigate some properties of the cohomological the theory of splittings of groups. Namely, we give a proof of the invariant E(G,W,M), defined in [5] and present related results with independence of E(G,W,M) with respect to the set of G-orbit representatives in W and properties of the invariant E(G,W,FTG) establishing a relation with the end of pairs of groups e˜(G,T), defined by Kropphller and Holler in [15]. The main results give necessary conditions for G to split over a subgroup T, in the cases where M=Z2(G/T) or M=FTG.
{"title":"Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups","authors":"E. L. C. Fanti, L. S. Silva","doi":"10.12958/ADM1246","DOIUrl":"https://doi.org/10.12958/ADM1246","url":null,"abstract":"Let us consider W a G-set and M a Z2G-module, where G is a group. In this paper we investigate some properties of the cohomological the theory of splittings of groups. Namely, we give a proof of the invariant E(G,W,M), defined in [5] and present related results with independence of E(G,W,M) with respect to the set of G-orbit representatives in W and properties of the invariant E(G,W,FTG) establishing a relation with the end of pairs of groups e˜(G,T), defined by Kropphller and Holler in [15]. The main results give necessary conditions for G to split over a subgroup T, in the cases where M=Z2(G/T) or M=FTG.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417186","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}
The famous Ukrainian mathematician and educator, Doctor of Physical and Mathematical Sciences, Professor Fedir Mykolayovych Lyman passed away on June 13, 2020 after a long illness.
{"title":"Fedir Mykolayovych Lyman (22.02.1941–13.06.2020)","authors":"Adm Editorial Board","doi":"10.12958/adm1749","DOIUrl":"https://doi.org/10.12958/adm1749","url":null,"abstract":"The famous Ukrainian mathematician and educator, Doctor of Physical and Mathematical Sciences, Professor Fedir Mykolayovych Lyman passed away on June 13, 2020 after a long illness.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419867","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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