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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Transitive group,Derangements,Polycirculant Conjecture
- چکیده:
- چکیده انگلیسی: Fixed-point-free permutations, also known as derangements, have been studied for centuries. In particular, depending on their applications, derangements of prime-power order and of prime order have always played a crucial role in a variety of different branches of mathematics: from number theory to algebraic graph theory. Substantial progress has been made on the study of derangements, many long-standing open problems have been solved, and many new research problems have arisen. The results obtained and the methods developed in this area have also effectively been used to solve other problems regarding finite vertex-transitive graphs. The methods used in this area range from deep group theory, including the classification of the finite simple groups, to combinatorial techniques. This article is devoted to surveying results, open problems and methods in this area.
- انتشار مقاله: 03-06-1397
- نویسندگان: Majid Arezoomand,Alireza Abdollahi,Pablo Spiga
- مشاهده
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Bi-Cayley graph,Integer eigenvalues,Representations of finite groups
- چکیده:
- چکیده انگلیسی: The bi-Cayley graph of a finite group $G$ with respect to a subset $Ssubseteq G$, which is denoted by $BCay(G,S)$, is the graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1), (sx,2)}mid xin G, sin S}$. A finite group $G$ is called a textit{bi-Cayley integral group} if for any subset $S$ of $G$, $BCay(G,S)$ is a graph with integer eigenvalues. In this paper we prove that a finite group $G$ is a bi-Cayley integral group if and only if $G$ is isomorphic to one of the groups $Bbb Z_2^k$, for some $k$, $Bbb Z_3$ or $S_3$.
- انتشار مقاله: 23-04-1393
- نویسندگان: Majid Arezoomand,Bijan Taeri
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Bi-Cayley graph,graph isomorphism,solvable group
- چکیده:
- چکیده انگلیسی: Let $S$ be a subset of a finite group $G$. The bi-Cayley graph $BCay(G,S)$ of $G$ with respect to $S$ is an undirected graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin G, sin S}$. A bi-Cayley graph $BCay(G,S)$ is called a BCI-graph if for any bi-Cayley graph $BCay(G,T)$, whenever $BCay(G,S)cong BCay(G,T)$ we have $T=gS^alpha$ for some $gin G$ and $alphain Aut(G)$. A group $G$ is called a BCI-group if every bi-Cayley graph of $G$ is a BCI-graph. In this paper, we prove that every BCI-group is solvable.
- انتشار مقاله: 22-01-1393
- نویسندگان: Majid Arezoomand,Bijan Taeri
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Bi-Cayley graph,Integer eigenvalues,Irreducible representation
- چکیده:
- چکیده انگلیسی: A graph is called integral if all eigenvalues of its adjacency matrix are integers. Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$. In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.
- انتشار مقاله: 02-01-1397
- نویسندگان: Majid Arezoomand,Bijan Taeri
- مشاهده