Mathematics > Combinatorics
[Submitted on 21 Dec 2018 (v1), last revised 2 Jan 2019 (this version, v2)]
Title:Further results on the least Q-eigenvalue of a graph with fixed domination number
View PDFAbstract: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.
Submission history
From: Guanglong Yu [view email][v1] Fri, 21 Dec 2018 03:52:06 UTC (19 KB)
[v2] Wed, 2 Jan 2019 11:11:51 UTC (19 KB)
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