Permanental bounds for the signless Laplacian matrix of bipartite graphs and unicyclic graphs

DOI10.1080/03081080903261467zbMath1239.05116OpenAlexW1998903385MaRDI QIDQ3082859

Li Zhang, Shuchao Li

Publication date: 17 March 2011

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081080903261467

zbMATH Keywords

treebipartite graphgirthpermanentsignless Laplacian matrixunicyclic graph

Mathematics Subject Classification ID

Trees (05C05) Determinants, permanents, traces, other special matrix functions (15A15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (12)

Graphs determined by the (signless) Laplacian permanental polynomials ⋮ Further results on the star degree of graphs ⋮ Permanental bounds for the signless Laplacian matrix of a unicyclic graph with diameter \(d\) ⋮ A study on determination of some graphs by Laplacian and signless Laplacian permanental polynomials ⋮ Computing the permanental polynomials of graphs ⋮ Graphs with least eigenvalue \(-2\): ten years on ⋮ Permanental bounds of the Laplacian matrix of trees with given domination number ⋮ On the (signless) Laplacian permanental polynomials of graphs ⋮ Extremal octagonal chains with respect to the coefficients sum of the permanental polynomial ⋮ A modified Grassmann algebra approach to theorems on permanents and determinants ⋮ The characterizing properties of (signless) Laplacian permanental polynomials of almost complete graphs ⋮ On the normalized Laplacian permanental polynomial of a graph

Cites Work

• The complexity of computing the permanent
• Permanent of the Laplacian matrix of trees and bipartite graphs
• Signless Laplacians of finite graphs
• Maximum permanents of matrices of zeros and ones
• Permanental polynomials of graphs
• Maximising the permanent and complementary permanent of (0,1)-matrices with constant line sum
• Which graphs are determined by their spectrum?
• Enumeration of cospectral graphs.
• Permanental bounds for nonnegative matrices via decomposition
• An upper bound for permanents of nonnegative matrices
• An update on Minc's survey of open problems involving permanents
• Eigenvalue bounds for the signless laplacian
• A characterization of the smallest eigenvalue of a graph
• New permanental upper bounds for nonnegative matrices
• Extending the minc-brègman upper bound for the permanent
• Bounds for permanents of non-negative matrices
• Upper bounds for permanents of $\left( {0,\,1} \right)$-matrices

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