Torsten Sander

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The unitary Cayley graph Xn has vertex set Zn = {0, 1, . . . , n−1}. Vertices a, b are adjacent, if gcd(a− b, n) = 1. For Xn the chromatic number, the clique number, the independence number, the diameter and the vertex connectivity are determined. We decide on the perfectness of Xn and show that all nonzero eigenvalues of Xn are integers dividing the value(More)
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(More)
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)
For every cograph there exist bases of the eigenspaces for the eigenvalues 0 and −1 that consist only of vectors with entries from {0, 1,−1}, a property also exhibited by other graph classes. Moreover, the multiplicities of the eigenvalues 0 and −1 of a cograph can be determined by counting certain vertices of the associated cotree.
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(More)
Today’s map navigation software offers more and more functionality. For example, it can not only route from a start to a destination address, but the user can also specify a number of via destinations that are to be visited along the route. What is not commonly found in the software is the handling of so-called stopover areas. Here the user specifies a(More)