Which numbers are status differences?

作者：

Highlights：

• The status difference is a graph invariant that found applications in communication networks and transportation networks.

• The numbers attainable as status differences of trees of fixed order are completely determined.

• The numbers attainable as status differences of connected graphs of fixed order are completely determined.

• The trees with the first a few smallest differences are characterized.

• Sharp upper bounds for the status difference are given over all trees with fixed parameters.

摘要

•The status difference is a graph invariant that found applications in communication networks and transportation networks.•The numbers attainable as status differences of trees of fixed order are completely determined.•The numbers attainable as status differences of connected graphs of fixed order are completely determined.•The trees with the first a few smallest differences are characterized.•Sharp upper bounds for the status difference are given over all trees with fixed parameters.

论文关键词：Status difference,Minimum status,Maximum status,Number of leaves,Diameter,Series-reduced tree

论文评审过程：Received 27 October 2020, Revised 14 January 2021, Accepted 17 January 2021, Available online 5 February 2021, Version of Record 5 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126004