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-G polygonal cactus is a connected graph in which the length of every cycle is k 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 n hexagons. (C) 2020 University of Kashan Press. All rights reserved