Maximal Independent Neighborhood Set of an Interval Graph

A graph G is an interval graph if there is a one-one correspondence between its vertices and a family I of intervals, such that two vertices in G are adjacent if and only if their corresponding intervals overlap. In this context, the family I of intervals is referred to as an interval model of G. Recently found minimum independent neighbourhood set of an interval graph. In this study, we exploit the Maximal Independent Neighbourhood Set (MLINS) of an interval graphs. This problem includes finding a maximal independent set, a shortest path between any two vertices in G in terms of directed network.