Computing the Permanent of the Laplacian Matrices of Nonbipartite Graphs | Zendy

Xiaoxue Hu | Zendy; Grace Kalaso | Zendy

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Computing the Permanent of the Laplacian Matrices of Nonbipartite Graphs

Author(s) -

Xiaoxue Hu,

Grace Kalaso

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/6621029

Subject(s) - mathematics , combinatorics , laplacian matrix , laplace operator , graph , recursion (computer science) , matrix (chemical analysis) , discrete mathematics , algorithm , mathematical analysis , materials science , composite material

Let G be a graph with Laplacian matrix L G . Denote by per L G the permanent of L G . In this study, we investigate the problem of computing the permanent of the Laplacian matrix of nonbipartite graphs. We show that the permanent of the Laplacian matrix of some classes of nonbipartite graphs can be formulated as the composite of the determinants of two matrices related to those Laplacian matrices. In addition, some recursion formulas on per L G are deduced.

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