Some New Results on Integer Additive Set-Valued Signed Graphs

2016/09/01 by Sudev, N. K., Ashraf, P. K., Germina, K. A.
#05C22 #05C78 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1609.00295

Abstract

Let X denotes a set of non-negative integers and \mathscrP(X) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective set-valued function f:V(G)→ \mathscrP(X)-\∅\ such that the induced function f⁺:E(G) → \mathscrP(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.

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