论文标题
关于直接产品的独立统治
On independent domination in direct products
论文作者
论文摘要
在\ cite {NR-1996} nowakowski和Rall列出了一系列涉及几种不同图形产品的猜想。特别是，他们猜想$ i（g \ times h）\ ge i（g）i（h）$，其中$ i（g）$是$ g $的独立支配数，$ g \ times h $是Graph $ g $和$ h $的直接产品。我们表明了这个猜想是错误的，实际上，构建了$ \ min \ {i（g），i（h）\} - i（g \ times h）$的图表对。当$ g $是路径或周期时，我们还会给出$ i（g \ times k_n）$的确切值。
In \cite{nr-1996} Nowakowski and Rall listed a series of conjectures involving several different graph products. In particular, they conjectured that $i(G\times H) \ge i(G)i(H)$ where $i(G)$ is the independent domination number of $G$ and $G\times H$ is the direct product of graphs $G$ and $H$. We show this conjecture is false, and, in fact, construct pairs of graphs for which $\min\{i(G), i(H)\} - i(G\times H)$ is arbitrarily large. We also give the exact value of $i(G\times K_n)$ when $G$ is either a path or a cycle.
