### Topological Integer Additive Set-Valued Graphs: A Review

#### Abstract

*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.

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