Integral Cayley Graphs Defined by Greatest Common Divisors
نویسندگان
چکیده
An undirected graph is called integral, if all of its eigenvalues are integers. Let Γ = Zm1 ⊗· · ·⊗Zmr be an abelian group represented as the direct product of cyclic groups Zmi of order mi such that all greatest common divisors gcd(mi,mj) ≤ 2 for i 6= j. We prove that a Cayley graph Cay(Γ, S) over Γ is integral, if and only if S ⊆ Γ belongs to the the Boolean algebra B(Γ) generated by the subgroups of Γ. It is also shown that every S ∈ B(Γ) can be characterized by greatest common divisors.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 18 شماره
صفحات -
تاریخ انتشار 2011