Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
Let G be a connected graph of order n. The remoteness of G, denoted by ρ, is the maximum average distance from a vertex to all other vertices. Let ∂1≥⋯≥∂n$\partial_{1}\geq\cdots\geq\partial_{n}$, ∂1L≥⋯≥∂nL$\partial_{1}^{L}\geq\cdots\geq\partial_{n}^{L}$ and ∂1Q≥⋯≥∂nQ$\partial_{1} ^{Q}\geq\cdots\geq\partial_{n}^{Q}$ be the distance, distance Laplacian and distance signless Laplacian eigenvalues of G, respectively. In this paper, we give lower bounds on ρ+∂1$\rho+\partial _{1}$, ρ−∂n$\rho-\partial_{n}$, ρ+∂1L$\rho+\partial_{1}^{L}$, ∂1L−ρ$\partial_{1} ^{L}-\rho$, 2ρ+∂1Q$2\rho+\partial_{1}^{Q}$ and ∂1Q−2ρ$\partial_{1}^{Q}-2\rho$ and the corresponding extremal graphs are also characterized.
Remoteness and distance eigenvalues of a graph
Let $G$ be a connected graph of order $n$ with diameter $d$. Remoteness $\rho$ of $G$ is the maximum average distance from a vertex to all others and $\partial_1\geq\cdots\geq \partial_n$ are the distance eigenvalues of $G$. In \cite{AH}, Aouchiche and Hansen conjectured that $\rho+\partial_3>0$ when $d\geq 3$ and $\rho+\partial_{\lfloor\frac{7d}{8}\rfloor}>0.$ In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on $\partial_n+\rho$ and $\partial_1-\rho$ when $G\ncong K_n$ and the extremal graphs are characterized.
Influence of naloxone on the antinociceptive effects of some antidepressant drugs.
The antinociceptive effects of tricyclic and atypical antidepressants were studied using the rat tail mechanical method. Clomipramine produced analgesia at the doses of 30 and 40 mg/kg, desimipramine at 10, 20 and 40 mg/kg, maprotiline at 20 and 30 mg/kg, mianserin at 30 mg/kg, nomifensine at 1, 2.5 and 5 mg/kg, indalpine at 10, 20 and 40 mg/kg, viloxazine at 60 and 80 mg/kg. Naloxone (0.8 mg/kg) abolished the antinociceptive action of these antidepressant drugs. These results suggest that the antinociceptive activity of these six antidepressant drugs in acute experimental pain could involve opiate mechanisms.