Torsten Sander

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The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime(More)
An undirected graph is called integral, if all of its eigenvalues are integers. Let Γ = Z m 1 ⊗ · · · ⊗ Z mr be an abelian group represented as the direct product of cyclic groups Z m i of order m i such that all greatest common divisors gcd(m i , m j) ≤ 2 for i = j. We prove that a Cayley graph Cay(Γ, S) over Γ is integral, if and only if S ⊆ Γ belongs to(More)