Edge-grafting theorems on permanents of the Laplacian matrices of graphs and their applications
Edge-grafting theorems on permanents of the Laplacian matrices of graphs and their applications
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DOI：
10.13001/1081-3810.1637
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发表时间：
2012-06
期刊：
影响因子：
--
通讯作者：
Shuchao Li;Yan Li
中科院分区：
文献类型：
--
作者：
Shuchao Li;Yan Li
研究了n元顶点上具有最小拉普拉斯恒等式的树，分别是单圈图。本文通过边嫁接变换，确定了给定二分划中具有第二和第三最小拉普拉斯恒等式的$n点树。类似地，刻划了具有第一、第二和第三最小拉普拉斯永久的给定二分划的$n$-点二部单圈图。从而确定了具有第一、第二和第三最小拉普拉斯恒等式的$n$-点二部单圈图。
The trees, respectively unicyclic graphs, on $n$ vertices with the smallest Laplacian permanent are studied. In this paper, by edge-grafting transformations, the $n$-vertex trees of given bipartition having the second and third smallest Laplacian permanent are identified. Similarly, the $n$-vertex bipartite unicyclic graphs of given bipartition having the first, second and third smallest Laplacian permanent are characterized. Consequently, the $n$-vertex bipartite unicyclic graphs with the first, second and third smallest Laplacian permanent are determined.