On the connectivity of $k$-distance graphs

Omid Khormali


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.


distance, radius, diameter, power graph

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DOI: http://dx.doi.org/10.5614/ejgta.2017.5.1.9


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