Connection graph of complete graphs with the maximum number of spanning trees

In this paper, using the electric circuit method, we consider a connection method of complete graphs by vertices or edges where the number of trees becomes the maximum. A necessary condition for the maximum number of trees is that both vertex and edge connection graphs are primitive connection graphs, and then the primitive connection graph is equivalent to its corresponding adjacency graph in regard to the number of trees. Therefore, we can use general graphs with the maximum number of trees to find the above-mentioned connection method of complete graphs.