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2004•Journal of Hefei University of TechnologyRequires access

The greatest eigenvalue of Laplacian matrices of bipartite graphs

Yin Jian-hong

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Abstract

The spectrum of Laplacian matrices of graphs has numerous applications in physics, chemistry, computer science, and many other sciences,but it is very difficult to compute the spectrum. In this paper,based on the analysis of the structure of bipartite graphs,the characteristic of Laplacian matrices of bipartite graphs is studied,and the new bounds for the greatest eigenvalue of Laplacian matrices of bipartite graphs are given according to the theory of nonnegative matrices.

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What this paper is about

The spectrum of Laplacian matrices of graphs has numerous applications in physics, chemistry, computer science, and many other sciences,but it is very difficult to compute the spectrum. In this paper,based on the analysis of the structure of bipartite graphs,the characteristic of Laplacian matrices of bipartite graphs is studied,and the new bounds for the greatest eigenvalue of Laplacian matrices of bipartite graphs are given according to the theory of nonnegative matrices.

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Available abstract

The spectrum of Laplacian matrices of graphs has numerous applications in physics, chemistry, computer science, and many other sciences,but it is very difficult to compute the spectrum. In this paper,based on the analysis of the structure of bipartite graphs,the characteristic of Laplacian matrices of bipartite graphs is studied,and the new bounds for the greatest eigenvalue of Laplacian matrices of bipartite graphs are given according to the theory of nonnegative matrices.

Key concepts: Bipartite graph, Eigenvalues and eigenvectors, Laplacian matrix, Laplace operator, Mathematics, Combinatorics, Spectrum (functional analysis), Discrete mathematics

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