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Omid Khormali
Department of Mathematical Sciences University of Montana, Missoula, MT 59812, USA
Electrical & Electronics Engineering

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On the connectivity of $k$-distance graphs Omid Khormali
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 1 (2017): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2017.5.1.9

Abstract

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.
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