Topological Integer Additive Set-Valued Graphs: A Review

Abstract Let  denote a set of non-negative integers and  be the collection of all non-empty subsets of . An integer additive set-labeling (IASL) of a graph  is an injective set-valued function  where induced function  is defined by , where  is the sumset of  and . A set-labeling  is said to be a topological set-labeling if  is a topology on the ground set  and a set-labeling  is said to be a topogenic set-labeling if  is a topology on . In this article, we critically review some interesting studies on the properties and characteristics of different topological and topogenic integer additive set-labeling of certain graphs. Keywords : Integer additive set-labeled graphs, topological additive set-labeled graphs, topogenic integer additive set-labeled graphs, integer additive set-filter graphs Cite this Article Sudev NK, Chithra KP, Germina KA. Topological Integer Additive Set-Valued Graphs: A Review. Research & Reviews: Discrete Mathematical Structures . 2017; 4(3): 1–17p.