$s$-Shunt Intersection Graph of a Graph

TL;DR

This paper introduces the concept of $s$-shunt intersection graphs, a new type of intersection graph derived from the $s$-arcs of a graph, expanding the study of intersection graph classes.

Contribution

It defines and initiates the study of $s$-shunt intersection graphs, a novel class based on $s$-arcs, contributing to the understanding of intersection graph variations.

Findings

Defined $s$-shunt intersection graphs from $s$-arcs.

Explored properties and structure of these graphs.

Laid groundwork for further research in this graph class.

Abstract

The intersection graph of a family of sets $\{S_{1},S_{2},\ldots,S_{n}\}$ is a graph whose vertex set is $\{S_{1},S_{2},\ldots,S_{n}\}$ and two distinct vertices are adjacent if the intersection of the corresponding sets is non-empty. Different types of intersection graphs have been studied depending on the nature of sets taken as the vertex set. A study on a particular type of intersection graph called $s$-shunt intersection graph, generated from the $s$-arcs of a given graph is initiated in this paper.