论文标题
在$ k $独立的图形产品上
On the $k$-independence number of graph products
论文作者
论文摘要
图形的$ k $独立数，$α_k（g）$，是一组在成对距离大于$ k $的顶点的最大大小，或者是$ k $ th power Graph $ g^k $的独立数。尽管众所周知，$α_k（g）=α（g^k）$，但通常，这对大多数图形产品都不成立，因此无法使用图形产品的$α$的现有界限。在本文中，我们介绍了几种图形产品的$ K $独立数量的尖锐上限。特别是，我们专注于笛卡尔，张量，强和词典产物。以前在文献中以$ k = 1 $为基础的一些界限是我们主要结果的推论。
The $k$-independence number of a graph, $α_k(G)$, is the maximum size of a set of vertices at pairwise distance greater than $k$, or alternatively, the independence number of the $k$-th power graph $G^k$. Although it is known that $α_k(G)=α(G^k)$, this, in general, does not hold for most graph products, and thus the existing bounds for $α$ of graph products cannot be used. In this paper we present sharp upper bounds for the $k$-independence number of several graph products. In particular, we focus on the Cartesian, tensor, strong, and lexicographic products. Some of the bounds previously known in the literature for $k=1$ follow as corollaries of our main results.
