On the connectivity of $k$-distance graphs

Omid Khormali (Department of Mathematical Sciences University of Montana, Missoula, MT 59812, USA)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 5, No 1 (2017): Electronic Journal of Graph Theory and Applications

For any $k \in \mathbb{N}$, the $k-$distance graph $D^{k}G$ has the same vertex set of $G$, and two vertices of $D^{k}G$ are adjacent if they are exactly distance $k$ apart in the original graph $G$. In this paper, we consider the connectivity of $D^{k}G$ and state the conditions for graph $G$ and integer $k$ such that the graph $D^{k}G$ is connected.