LAUSR

Let $G$ be a simple connected graph with $n$ vertices and $m$ edges and $d_{1}\geq d_{2}\geq \cdots \geq d_{n}>0$ its sequence of vertex degrees. If $\unicode[STIX]{x1D707}_{1}\geq \unicode[STIX]{x1D707}_{2}\geq \cdots \geq \unicode[STIX]{x1D707}_{n-1}>\unicode[STIX]{x1D707}_{n}=0$ are the Laplacian eigenvalues of $G$ , then the Kirchhoff index of $G$ is $\mathit{Kf}(G)=n\sum _{i=1}^{n-1}\unicode[STIX]{x1D707}_{i}^{-1}$ . We prove some new lower bounds for $\mathit{Kf}(G)$ in terms of some of the parameters $\unicode[STIX]{x1D6E5}=d_{1}$ , $\unicode[STIX]{x1D6E5}_{2}=d_{2}$ , $\unicode[STIX]{x1D6E5}_{3}=d_{3}$ , $\unicode[STIX]{x1D6FF}=d_{n}$ , $\unicode[STIX]{x1D6FF}_{2}=d_{n-1}$ and the topological index $\mathit{NK}=\prod _{i=1}^{n}d_{i}$ .