On the connectivity of k-distance graphs - Omid Khormali (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2017)
For any k N, the k-distance graph D^kG has the same vertex set of G, and two vertices of D^kG are adjacent if they are exactly distance k apart in the original graph G. In this paper, we consider the connectivity of D^kG and state the conditions for graph G and integer k such that the graph D^kG is connected.