FAIR DOMINATING SETS AND FAIR DOMINATION POLYNOMIAL OF A BANANA TREE

Abstract

Let  be a simple graph. A set  is a dominating set of  if every vertex not in  is adjacent to one or more vertices in . A dominating set  of  is a fair dominating set if every two vertices  are dominated by same number of vertices from . The minimum cardinality taken over all fair dominating sets in  is called the fair domination number of  and is denoted by . Let  be the banana tree of order . Let  be the family of fair dominating set of a banana tree  with cardinality , and let . In this paper we explore the fair domination polynomial of a banana tree and more properties are obtained in it.