Some New Results on Integer Additive SetValued Signed Graphs
Abstract
Let $X$ denotes a set of nonnegative integers and $\mathscr{P}(X)$ be its power set. An integer additive setlabeling (IASL) of a graph $G$ is an injective setvalued function $f:V(G)\to \mathscr{P}(X)\{\emptyset\}$ such that the induced function $f^+:E(G) \to \mathscr{P}(X)\{\emptyset\}$ is defined by $f^+(uv)=f(u)+f(v);\ \forall\, uv\in E(G)$, 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 $\sigma(uv)=(1)^{f^+(uv)};\ \forall\, uv\in E(\Sigma)$. In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive setlabelings.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.00295
 Bibcode:
 2016arXiv160900295S
 Keywords:

 Mathematics  General Mathematics;
 05C78;
 05C22
 EPrint:
 9 pages, Submitted to European J Pure. Appl. Math. arXiv admin note: text overlap with arXiv:1511.00678