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图的稀疏数的进一步研究

Further Studies on the Sparing Number of Graphs

N K Sudev, K A Germina

备注：
10 Pages, Submitted. arXiv admin note: substantial text overlap with arXiv:1310.6091
发表信息：
Tech S Vidya e-Journal of Research Vol. 2, 2014, pp.28-38
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摘要：

设$\mathbb{N}_0$表示所有非负整数的集合，$\mathcal{P}(\mathbb{N}_0)$表示它的幂集.整数加性集合索引器是内射函数$f:V(G)\to \mathcal{P}(\mathbb{N}_0)$，使得由$f^+ (uv) = f(u)+ f(v)$定义的诱导函数$f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$也是内射的，其中$f(u)+f(v)$是$f(u)$和$f(v)$的和集合。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。本文研究了弱整数可加集指标通过某些图和图运算的可容许性。

英文摘要：

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced 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 sum set of $f(u)$ and $f(v)$. 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 the admissibility of weak integer additive set-indexer by certain graphs and graph operations.

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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