Connectivity and diameter in distance graphs



For equation image and equation image, the distance graph Pmath image has vertex set {0,1,…,n − 1} and edge set {ij | 0 ≤ i,jn − 1,|ji| ∈ D}. The class of distance graphs generalizes the important and very well-studied class of circulant graphs, which have been proposed for numerous network applications. In view of fault tolerance and delay issues in these applications, the connectivity and diameter of circulant graphs have been studied in great detail. Our contributions are hardness results concerning computational problems related to the connectivity and the diameter of distance graphs and a characterization of the connected distance graphs Pmath image for |D| = 2. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(4), 310-315 2011