Minimum status, matching and domination of graphs

TL;DR

This paper establishes sharp bounds for the minimum status of connected graphs with fixed order and matching or domination numbers, characterizing extremal trees and identifying those with minimal minimum status.

Contribution

It provides new bounds for minimum status in graphs with fixed parameters and characterizes the extremal trees achieving these bounds.

Findings

Sharp upper bounds for minimum status with fixed order and matching number

Characterization of unique trees achieving the bounds

Identification of trees with minimal minimum status for given parameters

Abstract

The minimum status of a graph is the minimum of statuses of all vertices of this graph. We give a sharp upper bound for the minimum status of a connected graph with fixed order and matching number (domination number, respectively), and characterize the unique trees achieving the bound. We also determine the unique tree such that its minimum status is as small as possible when order and matching number (domination number, respectively) are fixed.