Minimal Harary index of unicyclic graphs with diameter at most 4

作者：

Highlights：

• We get the graphs minimizing the Harary index among unicyclic graphs with diameter 3 and 4, respectively.

• We present some graph transformations that decrease the Harary index of graphs.

• Almost all graph transformations in this paper can be generalized to more general graphs, which provide methods to determine the bounds of the Harary index of other classes of graphs.

摘要

•We get the graphs minimizing the Harary index among unicyclic graphs with diameter 3 and 4, respectively.•We present some graph transformations that decrease the Harary index of graphs.•Almost all graph transformations in this paper can be generalized to more general graphs, which provide methods to determine the bounds of the Harary index of other classes of graphs.

论文关键词：Unicyclic graphs,Harary index,Extremal graph

论文评审过程：Received 21 October 2019, Revised 4 April 2020, Accepted 11 April 2020, Available online 23 April 2020, Version of Record 23 April 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125315