On the Spectrum of Laplacian Matrix
Copyright policy )On the Spectrum of Laplacian Matrix
Let G be a simple graph of order n . The matrix ℒ G = D G − A G is called the Laplacian matrix of G , where D G and A G denote the diagonal matrix of vertex degrees and the adjacency matrix of G , respectively. Let l 1 G , l n − 1 G be the largest eigenvalue, the second smallest eigenvalue of ℒ G respectively, and λ 1 G be the largest eigenvalue of A G . In this paper, we will present sharp upper and lower bounds for l 1 G and l n − 1 G . Moreover, we investigate the relation between l 1 G and λ 1 G .
- Azarbaijan Shahid Madani University Iran (Islamic Republic of)
Eigenvalues, singular values, and eigenvectors, Graphs and linear algebra (matrices, eigenvalues, etc.)
Eigenvalues, singular values, and eigenvectors, Graphs and linear algebra (matrices, eigenvalues, etc.)
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