Nourishing Number of Flower-related Graphs


Keywords:
Flower-related graphs, strong integer additive set-indexers, nourishing number of a graph, sumsetAbstract
Let $\mathbb{N}_0 = \mathbb{N} \cup \left\lbrace 0\right\rbrace $ and $\mathcal{P}(\mathbb{N}_0)$ be the power set. If $f : V(G) \to \mathcal{P}(\mathbb{N}_0)$, then its induced map $f^+: E(G) \to \mathcal{P}(\mathbb{N}_0)$ is defined as $f^+(uv) = f(u)+f(v)$ where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. If $f$ and $f^+$ are injective, and $\left| f^+(uv)\right| = \left| f(u)\right| \left| f(v)\right| $ for all $uv$ in $E(G)$, then $f$ is a strong integer additive set-indexer of $G$. The nourishing number of $G$ is the least order of the maximal complete subgraph of $G$ such that $G$ admits a strong IASI. In this work, we compute the nourishing number of powers of flower-related graphs and graphs formed by duplicating each vertex in flower-related graphs by an edge.
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Copyright (c) 2023 International Journal of Mathematics And its Applications

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