R. Merris, Characteristic vertices of trees, Linear & Multilinear Algebra 22 (1987), 115-131. AMS Abstracts 8 (1987), 160. Research supported by ONR contract 85K0335. Math Reviews 89f: 05121.

Following M. Fiedler [Czech J. Math. 25 (1975), 607-618; and ibid. 619-633], the main thrust of this article concerns eigenvectors afforded by the algebraic connectivity (i.e., the smallest positive Laplacian eigenvalue) of a tree. Incidental to this work are a family of inequalities relating the coefficients of the chromatic polynomial and the Laplacian characteristic polynomial. Among the publications citing this article are

  • M. Fiedler, Linear & Multilinear Algebra 26 (1990), 85-106.
  • R. Grone, Linear Algebra Appl. 150 (1991), 167-178.
  • B. Mohar, Graph Theory, Combinatorics, and Applications (Y. Alavi, G. Chartrand, O. R. Ollermann, and A. J. Schwenk, eds.) Wiley, NY, 1991, pp 871-898.
  • B. Mohar, Graphs & Combinatorics 7 (1991), 53-64.
  • K. Balasubramanian, Chem. Phys. Lett. 224 (1994), 325-332.
  • K. Balasubramanian, Molecular Physics 85 (1995), 335-348.
  • K. Balasubramanian, J. Phys. Chem. 99 (1995), 6509-6518.
  • D. Cvetkovic, M. Doob, and H. Sachs, Spectra of Graphs, 3rd. ed., Johann Ambrosius Barth, Heidelberg, 1995.
  • P. F. Stadler, J. Mathematical Chemistry 20 (1996), 1-45.
  • S. Kirkland and M. Neumann, Linear & Multilinear Algebra 42 (1997), 187-203.
  • S. Fallat and S. Kirkland, Electronic J. Linear Algebra 3 (1998), 48-74.
  • S. Kirkland and S. Fallat, Linear & Multilinear Algebra 44 (1998), 131-148.
  • G. Zimmermann, Linear & Multilinear Algebra 45 (1998), 161-187.
  • R. B. Bapat and S. Pati, Linear & Multilinear Algebra 45 (1998), 247-273.
  • S. Kirkland, M. Neumann, and B. Shader, Czech. Math. J. 48 (1998), 65-76.
  • S. Kirkland, Czech. Math. J. 49 (1999), 617-632.
  • S. Kirkland, Linear & Multilinear Algebra 47 (2000), 93-103.
  • J. J. Molitierno and M. Neumann, Electronic J. Linear Algebra 8 (2001), 1-13.
  • S. Pati, Electronic J. Linear Algebra 8 (2001), 128-139.
  • S. M. Fallat, S. Kirkland, and S. Pati, Discrete Math 254 (2002), 115-142.
  • D. Barash, Nucleic Acids Research 31 (2003), 6578-6584.
  • J. J. Molitierno and M. Neumann, Linear & Multilinear Algebra 52 (2004), 145-156.
  • D. Barash, Bioinformatics 20 (2004), 1861-1869.
  • Y. Teranishi, Discrete Math. 290 (2005), 259-267.
  • Mei Lu, Huiqing Liu, and Feng Tian, Linear Algebra Appl. 402 (2005), 390-396.