A Note on Sparing Number Algorithm of Graphs

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.

6 pages, 2 figures, submitted

References in corpus (5)

• On Weakly Uniform Integer Additive Set-Indexers of Graphs
• On Integer Additive Set-Indexers of Graphs
• A Characterisation of Weak Integer Additive Set-Indexers of Graphs
• A Note on the Sparing Number of Graphs
• Further Studies on the Sparing Number of Graphs