Title of article :
Extremal Polygonal Cacti for Wiener Index and Kirchhoff Index
Author/Authors :
ZENG, MINGYAO Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Statistics - Hunan Normal University - Changsha - Hunan 410081 - P. R. China , XIAO, QIQI Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Statistics - Hunan Normal University - Changsha - Hunan 410081 - P. R. China , TANG, ZIKAI Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Statistics - Hunan Normal University - Changsha - Hunan 410081 - P. R. China , DENG, HANYUAN Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Statistics - Hunan Normal University - Changsha - Hunan 410081 - P. R. China
Abstract :
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 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.
Keywords :
Wiener index , Kirchhoff index , Cactus , Extremal graph
Journal title :
Iranian Journal of Mathematical Chemistry
