# On the connected and weakly convex domination numbers

## TL;DR

This paper investigates the relationship between connected and weakly convex domination numbers in graphs, identifying conditions for their equality and analyzing how edge removal affects the weakly convex domination number.

## Contribution

It establishes that the difference between these domination numbers can be arbitrarily large and characterizes graphs where they are equal, also examining the impact of edge removal.

## Key findings

- The difference between the numbers can be arbitrarily large.
- Weakly convex domination number equals connected domination number in certain graphs.
- Edge removal influences the weakly convex domination number as an interpolating function.

## Abstract

In this paper we study relations between connected and weakly convex domination numbers. We show that in general the difference between these numbers can be arbitrarily large and we focus on the graphs for which a weakly convex domination number equals a connected domination number. We also study the influence of the edge removing on the weakly convex domination number, in particular we prove that the weakly convex domination number is an interpolating function.