论文标题
部分可观测时空混沌系统的无模型预测
Characterizing and recognizing exact-distance squares of graphs
论文作者
论文摘要
对于图$ g =（v，e）$，其精确距离广场，$ g^{[\ sharp 2]} $，是带顶点set $ v $的图形，并且在$ x $ x $ x $和$ y $之间的边缘和$ x $和$ y $之间的边缘是$ y $，$ x $和y $ aken $ y $具有距离（确切的）$ 2 $ in $ g $。图$ g $是$ g^{[\ sharp 2]} $的精确距离平方根。我们给出具有精确距离平方根的图表的表征，我们的表征很容易导致多项式识别算法。我们表明，识别具有双分裂精确距离平方根的图是NP的完整。这两个结果对（通常）图形正方形的已知结果强烈对比。然后，我们将具有树作为精确距离平方根的图表表征，并从中获得这些图形的多项式时间识别算法。最后，我们表明，与通常的平方根不同，图可能具有（任意的许多）非晶状精确距离正方形的平方根，即树。
For a graph $G=(V,E)$, its exact-distance square, $G^{[\sharp 2]}$, is the graph with vertex set $V$ and with an edge between vertices $x$ and $y$ if and only if $x$ and $y$ have distance (exactly) $2$ in $G$. The graph $G$ is an exact-distance square root of $G^{[\sharp 2]}$. We give a characterization of graphs having an exact-distance square root, our characterization easily leading to a polynomial-time recognition algorithm. We show that it is NP-complete to recognize graphs with a bipartite exact-distance square root. These two results strongly contrast known results on (usual) graph squares. We then characterize graphs having a tree as an exact-distance square root, and from this obtain a polynomial-time recognition algorithm for these graphs. Finally, we show that, unlike for usual square roots, a graph might have (arbitrarily many) non-isomorphic exact-distance square roots which are trees.
