On some properties of distributed line graphs

Zhang and Liu introduced in 2012 a technique using distributed line graphs (DL graphs) to construct a DHT with constant size of routing information at each peer. They also introduced properties of DL graphs, but some results are described without detailed explanations and analysis. In this paper, we focus on the in-degree of a vertex (the number of edges coming towards the vertex) and the diameter (the maximum number of hops to reach the target) of a DL graph, and provide better results than previous ones, together with detailed proofs.