论文标题
统计和共同形图的枚举
Enumeration of cospectral and coinvariant graphs
论文作者
论文摘要
我们在最多10个具有相同频谱的图形（cosectral Mate）或至少具有相同的Smith正常形式（共同变形序列）相对于与图形相关的几个矩阵的连接图表上列出了枚举结果，至少有一个具有相同频谱的其他图（cospectral Mate），或者至少具有相同的Smith正常形式（共同形式）的其他图。目前的数据表明，距离拉普拉斯（Laplacian）的史密斯（Smith）正常形式和无标志的距离laplacian矩阵可能是在其他代数不变的情况下（例如从频谱中得出的代数不变的）失败的情况，可以区分图形。最后，我们使用史密斯（Smith）正常形式的距离距离laplacian矩阵的史密斯法线形式显示了一个新的图表。
We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (a cospectral mate), or at least one other graph with the same Smith normal form (coinvariant mate) with respect to several matrices associated to a graph. The present data give some indication that possibly the Smith normal form of the distance Laplacian and the signless distance Laplacian matrices could be a finer invariant to distinguish graphs in cases where other algebraic invariants, such as those derived from the spectrum, fail. Finally, we show a new graph characterization using the Smith normal form of the signless distance Laplacian matrix.
