On the minimum Kirchhoff index of graphs with a fixed number of cut vertices

Consider the family CC of all connected simple graphs on nn vertices which have kk cut-vertices. We state some properties of the graph in CC which has the minimum Kirchhoff index. In particular, we characterize this graph in the cases that k≤n2 or k≥n−3k≥n−3. Also we characterize the graph GG in CC having a non-cut-vertex with the lowest resistive eccentricity index among all non-cut-vertices of all graphs in CC.