A Classification of Finite Groups with Integral Bi-cayley Graphs
نویسندگان
چکیده
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 and only if G is isomorphic to one of the groups Z2 , for some k, Z3 or S3.
منابع مشابه
Finite groups admitting a connected cubic integral bi-Cayley graph
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.
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