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Geng, X., Hu, S. and Li, S. (2014) Permanental Bounds of the Laplacian Matrix of Trees with Given Domination Number. Graphs and Combinatorics, 31, 1423-1436.
https://doi.org/10.1007/s00373-014-1451-z

has been cited by the following article:

• TITLE: The Laplacian Permanents and Laplacian Ratios of Trees

  AUTHORS: Xiangshuai Dong

  KEYWORDS: Laplacian Permanents, Laplacian Ratio, Tree, Caterpillar

  JOURNAL NAME: Applied Mathematics, Vol.16 No.4, April 15, 2025

  ABSTRACT: Brualdi and Goldwasser characterized the Laplacian permanents of trees. In this paper, we study the Laplacian permanents of trees. We characterize some Laplacian permanents of trees. The Laplacian ratio of G is the Laplacian permanent of G divided by the product of degrees of all vertices. In this paper, we obtain that for any n -vertex caterpillar tree T , there exists an n -vertex caterpillar tree C n such that π( C n )≤π( T ) .