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Cash, G.G. and Gutman, I. (1990) The Laplacian Permanental Polynomial: Formulas and Algorithms. MATCH Communications in Mathematical and in Computer Chemistry, 51, 129-136.

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 ) .