A Study on Integer Additive Set-Valuations of Signed Graphs

Let $\mathbb{N}$ denote the set of all non-negative integers and $\text{cP}(\mathbb{N})$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\to \text{cP}(\mathbb{N})-\{\mathrm{\varnothing }\}$ such that the induced function $f^{+}:E(G)\to \text{cP}(\mathbb{N})-\{\mathrm{\varnothing }\}$ is defined by $f^+ (uv) = f(u)+ f(v)$,where$f(u)+f(v)$isthesumsetof$f(u)$and$f(v)$. A graph which admits an IASL is usually called an IASL-graph. An IASL $f$ of a graph $G$ is said to be an integer additive set-indexer (IASI) of $G$ if the associated function $f^{+}$ 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.