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Topological Integer Additive Set-Valued Graphs: A Review

N. K. Sudev, K. P. Chithra, K. A. Germina

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.



Keywords


Integer additive set-labeled graphs; topological additive set-labeled graphs; topogenic integer additive set-labeled graphs; integer additive set-filter graphs

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