A study on integer additive set-valuations of signed graphs

Keywords:
signed graphs, balanced signed graphs, clustering of signed graphs, IASL-signed graphs, strong IASL-signed graphs, weak IASL-signed graphs, isoarithmetic IASL-signed graphsAbstract
Let N0 denote the set of all non-negative integers and P(N0) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective set-valued function f:V(G)→P(N0)∖{∅} such that the induced function f+:E(G)→P(N0)∖{∅} 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 has 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.