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

Abstract

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

arXiv admin note: substantial text overlap with arXiv:1707.07123