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 σ defined by σ uv = −1 |f+ uv | ; ∀ uv ∈ E Σ . In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive set-labelings.