On hamiltonian Toeplitz graphs

In this paper we will consider hamiltonian properties of so-called Toeplitz graphs, which are defined as follows: Definition 1 Let n,m, a1, . . . , am ∈ N, 0 < a1 < · · · < am < n and V := {0, . . . , n− 1}. Define E := {[i, j] ∈ V 2 : ∃k ∈ {1, . . . , m} : |j − i| = ak}. Then the graph (V,E) with set of vertices V and set of edges E is called an undirected Toeplitz graph with entries (or stripes) a1, . . . , am. It is denoted by Tn(a1, . . . , am). The adjacency matrix of such a graph is usually called a symmetric Toeplitz matrix. Such matrices occur in many situations in pure and applied mathematics, we refer, for instance, to Gohberg [1]. 1 This research has been partially supported by the Spezialforschungsbereich F 003 “Optimierung und Kontrolle”/Projektbereich Diskrete Optimierung