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某些图的笛卡儿积的稀疏数

The Sparing Number of the Cartesian Products of Certain Graphs

K. P. Chithra, K. A. Germina, N. K. Sudev

备注：
8 pages, published. arXiv admin note: substantial text overlap with arXiv:1311.0858
发表信息：
Communications in Mathematics and Applications, Vol.5 Issue 1, 2014, 23-30
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摘要：

设$\mathbb{N}_0$是所有非负整数的集合.整数加性集合索引器（IASI）被定义为内射函数$f:V(G)\rightarrow \mathcal{P}(\mathbb{N}_0)$，使得由$f^+ (uv) = f(u)+ f(v)$定义的导出函数$f^+:E(G) \rightarrow \mathcal{P}(\mathbb{N}_0)$也是内射的，其中$f(u)+f(v)$是$f(u)$和$f(v)$的和集，$\mathcal{P}(\mathbb{N}_0)$是$\mathbb{N}_0$的幂集.如果是$f^+(uv)=k \forall ~ uv\in E(G)$，则称$f$是$k$ -均匀整数加性集合索引器。如果$|f^+(uv)|=max(|f(u)|,|f(v)|) \forall ~ uv\in E(G)$是整数加性集索引器，则称整数加性集索引器$f$是弱整数加性集索引器。本文研究了两个图的卡积的稀疏数。

英文摘要：

Let $\mathbb{N}_0$ be the set of all non-negative integers. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\rightarrow \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \rightarrow \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$ and $\mathcal{P}(\mathbb{N}_0)$ is the power set of $\mathbb{N}_0$. If $f^+(uv)=k \forall ~ uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^+(uv)|=max(|f(u)|,|f(v)|) \forall ~ uv\in E(G)$. In this paper, we study about the sparing number of the cartesian product of two graphs.

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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