关于可加集过滤图
On Integer Additive Set-Filtered Graphs
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.图$G$的整数可加集合标号（IASL）是一个内射函数$f:V(G)\to \mathcal{P}(\mathbb{N}_0)$，使得导出函数$f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$由$f^+ (uv) = f(u)+ f(v)$定义，其中$f(u)+f(v)$是$f(u)$和$f(v)$的和集.在本文中，我们引入了一种特殊类型的整数加性集指标的概念，称为整数加性集过滤标号的给定图，并研究了它们的特点。
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-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. In this paper, we introduce the notion of a particular type of integer additive set-indexers called integer additive set-filtered labeling of given graphs and study their characteristics.
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。
