R. Merris, The distance spectrum of a tree, J. Graph Theory 14 (1990), 365-369. AMS Abstracts 10 (1989), 401. Math Reviews 91h: 05085.

The main result of this article is an interlacing inequality involving the Distance and Laplacian eigenvalues of a tree. One consequence is a new proof that the chemical Wiener index of a tree on n vertices is n times the sum of the reciprocals of its nonzero Laplacian eigenvalues. (See number 78.)

Karen L. Collins [Discrete Math. 122 (1993), 103-112] has explained what was not clear to me in the sentence before Corollary 3 on p. 368.

Among the publications citing this article are

  • R. Grone, Linear Algebra Appl. 150 (1991), 167-178.
  • B. Mohar, Discrete Math. 109 (1992), 171-183.
  • K. L. Collins, Discrete Math. 122 (1993), 103-112.
  • B. Mohar and S. Poljak, Combinatorial and Graph-Theoretical Problems in Linear Algebra (R. A. Brualdi, et. al., eds.), Springer-Verlag, 1993, pp 107-151.
  • I. Gutman, Y. N. Yeh, S. L. Lee, and Y. L. Luo, Indian J. Chemistry (Section A), 32 (1993), 651-661.
  • I. Gutman, S. L. Lee, G. H. Chu, and Y. L. Luo, Indian J. Chemistry (Section A), 33 (1994), 603-608.
  • R. C. Entringer, A. Meir, J. W. Moon, and L. A. Szekely, Australasian J. Combinatorics 10 (1994), 211-224.
  • S. Markovic, I. Gutman, and Z. Bancevic, J. Serbian Chemical Soc. 60 (1995), 633-636.
  • J. W. Moon, Linear & Multilinear Algebra 39 (1995), 191-194.
  • D. M. Cvetkovic, M. Doob, and H. Sachs, Spectra of Graphs, 3rd ed., Johann Ambrosius Barth, Heidelberg, 1995.
  • R. B. Bapat, The Mathematics Student [Madras] 65 (1996), 214-223.
  • I. Gutman and B. Mohar, J. Chem. Inf. & Comp. Sci. 36 (1996), 982-985.
  • R. B. Bapat, Linear & Multilinear Algebra 42 (1997), 159-167.
  • A. A. Dobrynin, R. Entringer, and I. Gutman, Acta Applicandae Math 66 (2001), 211-249.
  • R. Bapat, S. J. Kirkland, and M. Neumann, Linear Algebra Appl. 401 (2005), 193-209.