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arXiv · 1812.08932

Further results on the least Q-eigenvalue of a graph with fixed domination number

Guanglong Yu·Yarong Wu·Mingqing Zhai
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Abstract

In this paper, we proceed on determining the minimum $q_{min}$ among the connected nonbipartite graphs on $n\geq 5$ vertices and with domination number $\frac{n+1}{3}<\gamma\leq \frac{n-1}{2}$. Further results obtained are as follows: $\mathrm{(i)}$ among all nonbipartite connected graph of order $n\geq 5$ and with domination number $\frac{n-1}{2}$, the minimum $q_{min}$ is completely determined; $\mathrm{(ii)}$ among all nonbipartite graphs of order $n\geq 5$, with odd-girth $g_{o}\leq5$ and domination number at least $\frac{n+1}{3}<\gamma\leq \frac{n-2}{2}$, the minimum $q_{min}$ is completely determined.

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Guanglong Yu, Yarong Wu, Mingqing Zhai. 2018-12-21. Further results on the least Q-eigenvalue of a graph with fixed domination number. https://arxiv.org/abs/1812.08932

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