A Study on Integer Additive Set-Valuations of Signed Graphs

Abstract

Let $\N$ denote the set of all non-negative integers and \cP(\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 \cP(\N)-\{\emptyset\} such that the induced function f^+:E(G) \to \cP(\N)-\{\emptyset\} is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ 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.Comment: 12 pages, Carpathian Mathematical Publications, Vol. 8, Issue 2, 2015, 12 page