Some new results on integer additive set-valued signed graphs

Abstract

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) ? P(X) ? {?} such that the induced function f+ : E(G) ? P(X) ? {?} is defined by f+(uv) = f(u) + f(v); ? uv ? 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 ? defined by ?(uv) = (?1)|f+(uv)|; ? uv ? E(?). In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive set-labelings.