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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2004.05435 |
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Table of Contents:
- The Knödel graph $W_{Δ,n}$ is a $Δ$-regular bipartition graph on $n\ge 2^Δ$ vertices and $n$ is an even integer. The vertices of $W_{Δ,n}$ are the pairs $(i,j)$ with $i=1,2$ and $0\le j\le n/2-1$. For every $j$, $0\le j\le n/2-1$, there is an edge between vertex $(1, j)$ and every vertex $(2,(j+2^k-1) \mod (n/2))$, for $k=0,1,\cdots,Δ-1$. In this paper we obtain some formulas for evaluating the distance of vertices of the Knödel graph and by them, we provide the formula $diam(W_{Δ,n})=1+\lceil\frac{n-2}{2^Δ-2}\rceil$ for the diameter of $W_{Δ,n}$, where $n\ge (2Δ-5)(2^Δ-2)+4$.