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arXiv · 1609.07247

On non-cyclic graph of finite groups

Ebrahim Vatandoost·Yasser Golkhandy Pour
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Abstract

Here we study some algebraic properties of non-cyclic graphs. In this paper we show that $\overline{\Gamma}_G$ is isomorphic to $K_3\cup (n-4)K_1$ or $K_4\cup (n-5)K_1$ if and only if $G$ is isomorphic to $D_8$ or $D_{10}$, respectively. We characterize all groups of order $n$ like $G$ in which $\gamma(\Gamma_G)+\gamma(\overline{\Gamma}_G)\in \{n, n-1, n-2, n-3\}$, where $|Cyc(G)|=1$.

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Ebrahim Vatandoost, Yasser Golkhandy Pour. 2016-09-23. On non-cyclic graph of finite groups. https://arxiv.org/abs/1609.07247

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