The first two cacti with larger multiplicative eccentricity resistance-distance

For a connected graph G, the multiplicative eccentricity resistance-distance ?*R(G) is defined as ?*R(G) = ?{x,y}?V(G)?(x)??(y)RG(x,y), where ?(?) is the eccentricity of the corresponding vertex and RG(x,y) is the effective resistance between vertices x and y. A cactus is a connected graph in which any two simple cycles have at most one vertex in common. Let Cat(n;t) be the set of cacti possessing n vertices and t cycles, where 0 ? t ? n-1/2. In this paper, we first introduce some edge-grafting transformations which will increase ?*R(G). As their applications, the extremal graphs with maximum and second-maximum ?*R(G)-value in Cat(n,t) are characterized, respectively.