An introduction to the mincut graph of a graph

TL;DR

This paper introduces the mincut graph, an intersection graph derived from a given graph, and explores its properties and implications within the broader context of graph operators and their fixed points.

Contribution

It presents the concept of the mincut graph, analyzes its characteristics, and addresses fundamental questions about its behavior under iteration and fixed points.

Findings

Defined the mincut graph and its properties

Explored fixed points and iteration effects of the mincut graph operator

Proposed future research directions for mincut graph analysis

Abstract

There is a well-documented research programme on graph operators which addresses questions such as `Which graphs appear as images of graphs?'; `Which graphs are fixed under the operator?'; `What happens if the operator is iterated?' In this paper, we introduce an intersection graph called the mincut graph and state its characteristics. We address some of the research programme questions for the mincut graph operator and conclude by stating further research questions on the mincut graph.