Topological Integer Additive Set-Valued Graphs: A Review

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

doi:10.37591/rrdms.v4i3.1054

Abstract

AbstractLet 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 ArticleSudev NK, Chithra KP, Germina KA. Topological Integer Additive Set-Valued Graphs: A Review. Research & Reviews: Discrete Mathematical Structures. 2017; 4(3): 1–17p.