Minimum status, matching and domination of graphs

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.