Abstract
In this paper, we study structural properties of Toeplitz graphs. We characterize Kq-free Toeplitz graphs for an integer q≥3 and give equivalent conditions for a Toeplitz graph Gn〈t1,t2,…,tk〉 with t1<⋯<tk and n≥tk−1+tk being chordal and equivalent conditions for a Toeplitz graph Gn〈t1,t2〉 being perfect. Then we compute the edge clique cover number and the vertex clique cover number of a chordal Toeplitz graph. Finally, we characterize the degree sequence (d1,d2,…,dn) of a Toeplitz graph with n vertices and show that a Toeplitz graph is a regular graph if and only if it is a circulant graph.
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