On Kirchhoff Index and Resistance-Distance Energy of a Graph

We report lower bounds for the Kirchhoff index of a connected (molecular) graph in terms of its structural parameters such as the number of vertices (atoms), the number of edges (bonds), maximum vertex degree (valency), second maximum vertex degree and minimum vertex degree. Also we give the Nordhaus–Gaddum-type result for Kirchhoff index. In this paper we define the resistance distance energy as the sum of the absolute values of the eigenvalues of the resistance distance matrix and also we obtain lower and upper bounds for this energy.