SOME NEW RESULTS ON INTEGER ADDITIVE SET-VALUED SIGNED GRAPHS

Let X denotes a set of non-negative integers and P(X) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective set-valued function f: V(G) [right arrow] P(X) - {[theta]} such that the induced function [f.sup.+]: E(G) [right arrow] P(X) - {[theta]} is defined by [f.sup.+] (uv) = f (u) + f (v); [for all] uv [member of] E(G), where f (u) + f (v) is the sumset of f (u) and f(v). An IASL of a signed graph is an IASL of its underlying graph G together with the signature [sigma] defined by [mathematical expression not reproducible]; [for all] uv [member of] E([summation]). In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive set-labelings. Keywords: Signed graphs; balanced signed graphs; clustering of signed graphs; integer additive set-labeled signed graphs; arithmetic integer additive set-labeled signed graphs. AMS Subject Classification: 05C78, 05C22.