  Given a connected graph $G$, the toughness $\tau_G$ is defined as the minimum
value of the ratio $|S|/\omega_{G-S}$, where $S$ ranges over all vertex cut
sets of $G$, and $\omega_{G-S}$ is the number of connected components in the
subgraph $G-S$ obtained by deleting all vertices of $S$ from $G$. In this
paper, we provide a lower bound for the toughness $\tau_G$ in terms of the
maximum degree, minimum degree and normalized Laplacian eigenvalues of $G$.
This can be viewed as a slight generalization of Brouwer's toughness
conjecture, which was confirmed by Gu (2021). Furthermore, we give a
characterization of those graphs attaining the two lower bounds regarding
toughness and Laplacian eigenvalues provided by Gu and Haemers (2022).
