Ordering trees by algebraic connectivity

@article{Grone1990OrderingTB,
  title={Ordering trees by algebraic connectivity},
  author={Robert Grone and Russell Merris},
  journal={Graphs and Combinatorics},
  year={1990},
  volume={6},
  pages={229-237}
}
Let G be a graph on n vertices. Denote by L(G) the difference between the diagonal matrix of vertex degrees and the adjacency matrix. It is not hard to see that L(G) is positive semidefinite symmetric and that its second smallest eigenvalue, a(G) > 0, if and only if G is connected. This observation led M. Fiedler to call a(G) the algebraic connectivity of G. Given two trees, T i and T2, the authors explore a graph theoretic interpretation for the difference between a(T~) and a(T2). Let G = (V… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 17 references

Recent Results in the Theory of Graph Spectra

  • D. Cvetkovi, M. Doob, I. Gutman, A. Torgasev
  • Amsterdam: North-Holland,
  • 1988

Algebraic connectivity oftrees

  • R. Grone, R. Merris
  • Czech. Math. J. 37(112), 660-670
  • 1987
2 Excerpts

Characteristic vertices of trees

  • R. Merris
  • Linear Multilinear Algebra 22,
  • 1987
2 Excerpts

A bound for the permanent of the Laplacian matrix

  • R. B. Bapat
  • Linear Algebra Appl. 74, 219 223
  • 1986

Principal subpermanents of the Laplacian matrix

  • A. Vrba
  • Linear Multilinear Algebra 19,
  • 1986

The permanent of the Laplacian matrix of a bipartite graph

  • A. Vrba
  • Czech. Math. J. 36(111), 7-17
  • 1986

Eigenvalues of the Laplacian of a graph

  • Anderson, W. N., T. D. Morley
  • Linear and Multilinear Algebra 18, 141-145
  • 1985

Permanental roots and the star degree of a graph

  • I. Faria
  • Linear Algebra Appl. 64, 255 265
  • 1985

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