On the extremal graphs with respect to the total reciprocal edge-eccentricity

The total reciprocal edge-eccentricity of a graph G is defined as xi(ee)(G) = Sigma(u is an element of VG) d(G)(u)/epsilon(G)(u), where d(G)(u) is the degree of u and epsilon(G)(u) is the eccentricity of u. In this paper, we first characterize the unique graph with the maximum total reciprocal edge-eccentricity among all graphs with a given number of cut vertices. Then we determine the k-connected bipartite graphs of order n with diameter d having the maximum total reciprocal edge-eccentricity. Finally, we identify the unique tree with the minimum total reciprocal edge-eccentricity among the n-vertex trees with given degree sequence.