Integral Cayley Graphs and Groups
نویسندگان
چکیده
منابع مشابه
Integral Quartic Cayley Graphs on Abelian Groups
A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine integral quartic Cayley graphs on finite abelian groups. As a side result we show that there are exactly 27 connected integral Cayley graphs up to 11 vertices.
متن کاملIntegral Cayley Graphs over Abelian Groups
Let Γ be a finite, additive group, S ⊆ Γ, 0 6∈ S, − S = {−s : s ∈ S} = S. The undirected Cayley graph Cay(Γ, S) has vertex set Γ and edge set {{a, b} : a, b ∈ Γ, a − b ∈ S}. A graph is called integral, if all of its eigenvalues are integers. For an abelian group Γ we show that Cay(Γ, S) is integral, if S belongs to the Boolean algebra B(Γ) generated by the subgroups of Γ. The converse is proven...
متن کاملIntegral Sets and Cayley Graphs of Finite Groups
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 کاملGroups all of whose undirected Cayley graphs are integral
Let G be a finite group, S ⊆ G \ {1} be a set such that if a ∈ S, then a−1 ∈ S, where 1 denotes the identity element of G. The undirected Cayley graph Cay(G, S) ofG over the set S is the graphwhose vertex set is G and two vertices a and b are adjacent whenever ab−1 ∈ S. The adjacency spectrum of a graph is the multiset of all eigenvalues of the adjacency matrix of the graph. A graph is called i...
متن کاملA Classification of Finite Groups with Integral Bi-cayley Graphs
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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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2014
ISSN: 0895-4801,1095-7146
DOI: 10.1137/130925487