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16 February 2025
 
  » arxiv » 1609.0295

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Some New Results on Integer Additive Set-Valued Signed Graphs
N. K. Sudev ; P. K. Ashraf ; K. A. Germina ;
Date 1 Sep 2016
AbstractLet $X$ denotes a set of non-negative integers and $mathscr{P}(X)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G) o mathscr{P}(X)-{emptyset}$ such that the induced function $f^+:E(G) o mathscr{P}(X)-{emptyset}$ is defined by $f^+(uv)=f(u)+f(v); forall, uvin E(G)$, 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 $sigma(uv)=(-1)^{|f^+(uv)|}; forall, uvin E(Sigma)$. In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive set-labelings.
Source arXiv, 1609.0295
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