On the diameter of total domination vertex critical graphs

TL;DR

This paper investigates the diameters of various types of domination vertex critical graphs, providing upper bounds and identifying sharp bounds for some cases, advancing understanding of their structural properties.

Contribution

It offers new upper bounds on the diameter of total domination vertex critical graphs and related types, with some bounds proven to be sharp.

Findings

Upper bounds on diameters established

Two bounds proven to be sharp

Enhanced understanding of graph structure

Abstract

In this paper, we consider various types of domination vertex critical graphs, including total domination vertex critical graphs, independent domination vertex critical graphs and connected domination vertex critical graphs. We provide upper bounds on the diameter of them, two of which are sharp.