Cayley graphs of finite groups
نویسندگان
چکیده
منابع مشابه
On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian
In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.
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The bi-Cayley graph of a finite group G with respect to a subset S ⊆ G, which is denoted by BCay(G,S), is the graph with vertex set G× {1, 2} and edge set {{(x, 1), (sx, 2)} | x ∈ G, s ∈ S}. A finite group G is called a 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 a...
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Integral sets of finite groups are discussed and related to the integral Cayley graphs. The Boolean algebra of integral sets are determined for dihedral group and finite abelian groups. We characterize the finite abelian groups as those finite groups where the Boolean algebra generated by integral sets equals the Boolean algebra generated by its subgroups.
متن کاملOn locally primitive Cayley graphs of finite simple groups
A graph /is said to be G-locally primitive, where G is a subgroup of automorphisms of /-, if the stabiliser G~ of a vertex a acts primitively on the s e t / ( a ) of vertices of / adjacent to or. For a finite non-abelian simple group L and a Cayiey subset S of L, suppose that L <3 G...<Aut( L ) , and the Cayley graph /= Cay ( L, S) is G-locally primitive. In this paper we prove that L is a simp...
متن کاملNORMAL 6-VALENT CAYLEY GRAPHS OF ABELIAN GROUPS
Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90033-6