Extreme Values of the Fiedler Vector on Trees

M. Fiedler. Algebraic connectivity of graphs. Czechoslovak Math. J., 23(98):298–305, 1973

1973

Earlier work this paper cites.

F. Harary and A. Schwenk, The number of caterpillars, Discrete Mathematics, 6 (4): 359–365 (1973)

1973

Earlier work this paper cites.

M. Fiedler. A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory. Czechoslovak Math. J., 25(100)(4):619–633, 1975

1975

Earlier work this paper cites.

S. El-Basil. Applications of caterpillar trees in chemistry and physics. J. Math. Chem., 1(2):153–174, Jul 1987

1987

Earlier work this paper cites.

R. Merris, Characteristic vertices of trees. Linear and Multilinear Algebra 22 (1987), no. 2, 115–131

1987

Earlier work this paper cites.

M. Fiedler. Laplacian of graphs and algebraic connectivity. In Combinatorics and graph theory (Warsaw, 1987), volume 25 of Banach Center Publ., pages 57–70. PWN, Warsaw, 1989

1989

Earlier work this paper cites.

B. Mohar, Eigenvalues, diameter, and mean distance in graphs. Graphs Combin. 7 (1991), no. 1, 53–64

1991

Earlier work this paper cites.

B. Mohar, Laplace eigenvalues of graphs–a survey. Algebraic graph theory (Leibnitz, 1989). Discrete Math. 109 (1992), no. 1-3, 171–183

1992

Earlier work this paper cites.

R. Merris, Laplacian matrices of graphs: a survey. Second Conference of the International Linear Algebra Society (ILAS) (Lisbon, 1992). Linear Algebra Appl. 197/198 (1994), 143–176

1994

Earlier work this paper cites.

S. Kirkland, M. Neumann and B. Shader, Characteristic vertices of weighted trees via Perron values. Linear and Multilinear Algebra 40 (1996), no. 4, 311–325

1996

Earlier work this paper cites.

M. Taylor, Partial differential equations. II. Qualitative studies of linear equations. Applied Mathematical Sciences, 116. Springer-Verlag, New York, 1996

1996

Earlier work this paper cites.

F. R. Chung, Spectral Graph Theory. CBMS Regional Conference Series in Mathematics, 92. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1997

1997

Earlier work this paper cites.

S. Kirkland and M. Neumann, Michael, Algebraic connectivity of weighted trees under perturbation. Linear and Multilinear Algebra 42 (1997), no. 3, 187–203

1997

Earlier work this paper cites.

S. Fallat and S. Kirkland, Extremizing algebraic connectivity subject to graph-theoretic constraints. Electron. J. Linear Algebra 3 (1998), 48–74

1998

Cited alongside, same era.

S. Kirkland and S. Fallat, Perron components and algebraic connectivity for weighted graphs. Linear and Multilinear Algebra 44 (1998), no. 2, 131–148

1998

Cited alongside, same era.

K. Burdzy and W. Werner, A counterexample to the ”hot spots” conjecture, Ann. Math. 149 (1999), p. 309–317

1999

Cited alongside, same era.

R. Bapat, S. Kirkland and S. Pati, The perturbed Laplacian matrix of a graph. Linear and Multilinear Algebra 49 (2001), no. 3, 219–242

2001

Cited alongside, same era.

E. Brian Davies, G. Gladwell, J. Leydold and P. Stadler, Discrete nodal domain theorems. Linear Algebra Appl. 336 (2001), 51–60

2001

Cited alongside, same era.

D. Shuman, S. Narang, P. Frossard, A. Ortega and P. Vandergheynst, The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains, IEEE Signal Processing Magazine 30, p. 83–98, (2013)

2013

Later among the works it cites.

R. Band, The nodal count 0, 1, 2, 3,… implies the graph is a tree. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 372 (2014), 20120504

2014

Later among the works it cites.

J. Irion and N. Saito, Hierarchical graph Laplacian eigen transforms. JSIAM Lett. 6, 21–24, (2014)

2014

Later among the works it cites.

I. Rocha and V. Trevisan, A Fiedler-like theory for the perturbed Laplacian. Czechoslovak Math. J. 66(141) (2016), no. 3, 717–735

2016

Later among the works it cites.

D. Shuman, M. Faraji and P. Vandergheynst, Multiscale Pyramid transform for graph signals, IEEE Transactions on Signal Processing 64, p. 2119–2134, (2016)