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Article overview
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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 | Abstract: | Let $X$ 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 | Services: | Forum | Review | PDF | Favorites |
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