Weak Integer Additive Set-Indexers of Certain Graph Products
DOI:
https://doi.org/10.26713/jims.v6i1.236Abstract
Let $\matbb{N}_0$ be the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) is dened as an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G)\to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+(uv) = f(u) + f(v)$ is also injective, where $f(u) + f(v)$ is the sumset of $f(u)$ and $f(v)$. An IASI f is said to be a weak IASI if $|f^+(uv)| = \max(|f(u)|,|f(v)|)$ $\forall$ $uv \in E(G)$. In this paper, we study the admissibility of weak IASI by certain graph products of two weak IASI graphs.
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