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arXiv · 1706.00863

On the reduced Euler characteristic of independence complexes of circulant graphs

Giancarlo Rinaldo·Francesco Romeo
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Abstract

Let $G$ be the circulant graph $C_n(S)$ with $S\subseteq\{ 1,\ldots,\left \lfloor\frac{n}{2}\right \rfloor\}$. We study the reduced Euler characteristic $\tildeχ$ of the independence complex $Δ(G)$ for $n=p^k$ with $p$ prime and for $n=2p^k$ with $p$ odd prime, proving that in both cases $\tildeχ$ does not vanish. We also give an example of circulant graph whose independence complex has $\tildeχ$ equals to $0$, giving a negative answer to R. Hoshino.

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Giancarlo Rinaldo, Francesco Romeo. 2018-04-12. On the reduced Euler characteristic of independence complexes of circulant graphs. https://arxiv.org/abs/1706.00863

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