Cacti with maximum eccentricity resistance-distance sum

The eccentricity resistance-distance sum of a connected graph G is defined as ξR(G)=∑u,v∈V(G)(ε(u)+ε(v))R(u,v), where ε(u) is the eccentricity of the vertex u and R(u,v) is the resistance distance between u and v in graph G. Let Cat(n;t) be the set of all cacti possessing n vertices and t cycles. In this paper, some transformations of a connected graph are studied, which is mainly focused on the monotonicity on the eccentricity resistance-distance sum. By the transformation, the extremal graphs with maximum ξR-value of Cat(n;t) are characterized.