$s$-Shunt Intersection Graph of a Graph

Abstract

The intersection graph of a family of sets $\{S_1,S_2,\dots ,S_n\}$ is a graph whose vertex set is $\{S_1,S_2,\dots ,S_n\}$ 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.