# Bipartization of graphs

## TL;DR

This paper introduces a new characterization of bipartite graphs where the domination number equals the size of the smaller part, using a novel graph operation to deepen understanding of domination properties.

## Contribution

It presents a new characterization of certain bipartite graphs based on a novel graph operation, advancing the theoretical understanding of domination numbers.

## Key findings

- Characterization of bipartite graphs with domination number equal to the smaller part's size
- Introduction of a new graph operation for analyzing domination properties
- Theoretical insights into domination number in bipartite graphs

## Abstract

A dominating set of a graph $G$ is a set $D\subseteq V_G$ such that every vertex in $V_G-D$ is adjacent to at least one vertex in $D$, and the domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set of $G$. In this paper we provide a new characterization of bipartite graphs whose domination number is equal to the cardinality of its smaller partite set. Our characterization is based upon a new graph operation.