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关于图的稀疏数的一个注记

A Note on the Sparing Number of Graphs

N. K. Sudev, K. A. Germina

备注：
10 pages, 10 figures, submitted
发表信息：
Advances and Applications in Discrete Mathematics, Vol.14 Issue.1, 2014, pp.51-65
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摘要：

整数加性集合索引器被定义为内射函数$f:V(G)\rightarrow 2^{\mathbb{N}_0}$，使得由$g_f (uv) = f(u)+ f(v)$定义的诱导函数$g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$也是内射的。如果所有$u,v\in V(G)$都满足$|g_f(uv)|=max(|f(u)|,|f(v)|)$，则称IASI $f$为弱IASI。允许弱IASI的图可以称为弱IASI图。图$G$的一个元素，一个顶点或一条边的集索引数是它的集标号的基数。图$G$的稀疏数是图$G$允许弱IASI所需的具有单例集标签的边的最小数目。本文研究了某些图的稀疏数以及稀疏数与匹配数、色数、覆盖数、独立数等参数的关系。

英文摘要：

An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective. An IASI $f$ is said to be a weak IASI if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph $G$, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph $G$ is the minimum number of edges with singleton set-labels, required for a graph $G$ to admit a weak IASI. In this paper, we study the sparing number of certain graphs and the relation of sparing number with some other parameters like matching number, chromatic number, covering number, independence number etc.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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