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Mathematics 2015, 3(1), 29-39; doi:10.3390/math3010029

# A Study on the Nourishing Number of Graphs and Graph Powers

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Department of Mathematics, Vidya Academy of Science & Technology, Thalakkottukara, Thrissur 680501, Kerala, India
2
PG & Research Department of Mathematics, Mary Matha Arts & Science College, Mananthavady, Wayanad 670645, Kerala, India
*
Author to whom correspondence should be addressed.
Received: 17 January 2015 / Accepted: 2 March 2015 / Published: 6 March 2015

# Abstract

Let $$\mathbb{N}_{0}$$ be the set of all non-negative integers and $$\mathcal{P}(\mathbb{N}_{0})$$ be its power set. Then, an integer additive set-indexer (IASI) of a given graph $$G$$ is defined as an injective function $$f:V(G)\to \mathcal{P}(\mathbb{N}_{0})$$ such that the induced edge-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 $$f$$ of $$G$$ is said to be a strong IASI of $$G$$ if $$|f^+(uv)|=|f(u)|\,|f(v)|$$ for all $$uv\in E(G)$$. The nourishing number of a graph $$G$$ is the minimum order of the maximal complete subgraph of $$G$$ so that $$G$$ admits a strong IASI. In this paper, we study the characteristics of certain graph classes and graph powers that admit strong integer additive set-indexers and determine their corresponding nourishing numbers. View Full-Text
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Naduvath, S.; Augustine, G. A Study on the Nourishing Number of Graphs and Graph Powers. Mathematics 2015, 3, 29-39.

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