A Study on Integer Additive Set-Valuations of Signed Graphs
N. K. Sudev, K. A. Germina

TL;DR
This paper explores integer additive set-labelings of signed graphs, introducing new definitions and analyzing properties of graphs that admit such labelings, expanding the understanding of set-labeling in signed graph theory.
Contribution
It defines integer additive set-labelings for signed graphs and investigates properties of graphs that admit these labelings, providing new theoretical insights.
Findings
Characterization of signed graphs with integer additive set-labelings
Conditions for the existence of integer additive set-indexers in signed graphs
Properties of signed graphs admitting specific set-labelings
Abstract
Let denote the set of all non-negative integers and be its power set. An integer additive set-labeling (IASL) of a graph is an injective set-valued function such that the induced function is defined by , where is the sumset of and . A graph which admits an IASL is usually called an IASL-graph. An IASL of a graph is said to be an integer additive set-indexer (IASI) of if the associated function is also injective. In this paper, we define the notion of integer additive set-labeling of signed graphs and discuss certain properties of signed graphs which admits certain types of integer additive set-labelings.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · graph theory and CDMA systems
