Extremal polygonal cacti for Wiener index and Kirchhoff index

Document Type : Research Paper

Authors

Hunan Normal University

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

References

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Iranian Journal of Mathematical Chemistry
Volume 11, Issue 3
September 2020
Pages 201-211

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