extremal polygonal cacti for wiener index and kirchhoff index

For a connected graph g ,the wiener index w(g) of g is the sum of the distances of all pairs of vertices, the kirchhoff index kf (g)of g is the sum of the resistance distances of all pairs of vertices. a ݇k- polygonal cactus is a connected graph in which the length of every cycle is ݇ and any two cycles have at most one common vertex. in this paper, we give the maximum and minimum values of the wiener index and the kirchhoff index for all k-polygonal cacti with n cycles and determine the corresponding extremal graphs, generalize results of spiro hexagonal chains with ݊ hexagons.