The Sparing Number of the Cartesian Product of Certain Graphs
DOI:
https://doi.org/10.26713/cma.v5i1.231Keywords:
Integer additive set-indexers, mono-indexed elements of a graphs, weak integer additive set-indexers, sparing number of a graphAbstract
Let $\mathbb{N}_0$ be the set of all non-negative integers. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\rightarrow \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \rightarrow \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$ and $\mathcal{P}(\mathbb{N}_0)$ is the power set of $\mathbb{N}_0$. If $f^+(uv)=k~\forall~uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^+(uv)|=max(|f(u)|,|f(v)|)~\forall ~ uv\in E(G)$. In this paper, we study about the sparing number of the cartesian product of two graphsDownloads
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