ON TOPOLOGICAL INTEGER ADDITIVE SET-LABELING OF GRAPHS

Abstract

 Extending the concepts of IASL and topological set-labeling, Sudev and Germina have introduced TIASL in 2015. For a graph  and a non-empty set , a TIASL is defined as a mapping  such that  is one-one, the function induced  given by  is well-defined (where the operation  between two sets is defined as sumset of two sets) and  is a topology on . The set  used here is known as ground set. In this paper, we give necessary and sufficient conditions for the given graph to admit TIASL with given non-empty set as a ground set. We also discuss embedding of graphs into TIASL graphs. We also give a formula to find topological set-labeling numbers of TIASL graphs.