A Note on Sparing Number Algorithm of Graphs

N. K. Sudev; K. A. Germina

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arXiv · 1512.01113

A Note on Sparing Number Algorithm of Graphs

N. K. Sudev·K. A. Germina

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Abstract

Let $X$ denote a set of all non-negative integers and $\sP(X)$ be its power set. A weak integer additive set-labeling (WIASL) of a graph $G$ is an injective set-valued function $f:V(G)\to \sP(X)-\{\emptyset\}$ where induced function $f^+:E(G) \to \sP(X)-\{\emptyset\}$ is defined by $f^+ (uv) = f(u)+ f(v)$ such that either $|f^+ (uv)|=|f(u)|$ or $|f^+ (uv)|=|f(v)|$ , where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. The sparing number of a WIASL-graph $G$ is the minimum required number of edges in $G$ having singleton set-labels. In this paper, we discuss an algorithm for finding the sparing number of arbitrary graphs.

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BibTeX RIS

N. K. Sudev, K. A. Germina. 2015-12-02. A Note on Sparing Number Algorithm of Graphs. https://arxiv.org/abs/1512.01113

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