Computing the permanental polynomials of graphs

Xiaogang Liu and Tingzeng Wu

Applied Mathematics and Computation, 2017, vol. 304, issue C, 103-113

Abstract: Let M be an n × n matrix with entries mij (i,j=1,2,…,n). The permanent of M is defined to be per(M)=∑σ∏i=1nmiσ(i),where the sum is taken over all permutations σ of {1,2,…,n}. The permanental polynomial of M is defined by per(xIn−M), where In is the identity matrix of size n. In this paper, we give recursive formulas for computing permanental polynomials of the Laplacian matrix and the signless Laplacian matrix of a graph, respectively.

Keywords: Permanent; Laplacian matrix; Signless Laplacian matrix; Laplacian permanental polynomial; Signless Laplacian permanental polynomial (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:304:y:2017:i:c:p:103-113

DOI: 10.1016/j.amc.2017.01.052

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