On the extremal graphs of diameter 2 with respect to the eccentric resistance-distance sum

Given a connected graph G, the eccentric resistance-distance sum of G is defined as ξR(G)=∑{u,v}⊆VG(εG(u)+εG(v))Ruv, where εG(⋅) is the eccentricity of the corresponding vertex and Ruv is the resistance-distance between u and v in G. In this paper, the graphs of diameter 2 with the largest, second largest, third largest, smallest, second smallest and third smallest eccentric resistance-distance sums are identified, respectively. The main tools are standard results of electrical networks.