The ρ‐-moments of vertex‐weighted graphs

作者：

Highlights：

• Three graft operations are introduced, which can be seen as some extensions of the hierarchical product.

• The explicit formulas for computing the ρ-moments of three classes of hereditary graphs are given, by which the order relations on ρ-moments of the uniform(non-uniform) cactus chains are also given.

• The maximum(minimum) ρ-moment polyphenyl chains, maximum(minimum) ρ-moment spiro chains etc are obtained, respectively. This generalizes the results of Deng (2012).

摘要

•Three graft operations are introduced, which can be seen as some extensions of the hierarchical product.•The explicit formulas for computing the ρ-moments of three classes of hereditary graphs are given, by which the order relations on ρ-moments of the uniform(non-uniform) cactus chains are also given.•The maximum(minimum) ρ-moment polyphenyl chains, maximum(minimum) ρ-moment spiro chains etc are obtained, respectively. This generalizes the results of Deng (2012).

论文关键词：Topological index,Moment,Vertex-weighted graph,Extremal problem

论文评审过程：Received 29 October 2020, Revised 16 January 2021, Accepted 4 February 2021, Available online 23 February 2021, Version of Record 23 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126070