Algorithms for finding a Neighbourhood Total Restrained Dominating Set of Interval Graphs and Circular-Arc Graphs

Abstract

A set  is a neighbourhood total restrained dominating set of a graph  if all the vertices in  has one or more adjacent vertex in  as well as in  and also the each vertex in  is adjacent to at least a vertex in  and if the induced sub-graph  has no isolated vertex. The cardinality of a minimum total restrained dominating set  is called total restrained dominating number and is represented as .

In this paper, we are introducing Neighborhood total restrained domination and develop an algorithm to find neighbourhood total restrained dominating set for Interval graphs and circular-arc graphs.