A minimax-condition for the characteristic center of a tree

References

• Anderson , W. N. Jr. and Morley , T. D. 1985 . Eigenvalues of the Laplacian of a graph . Linear and Multilinear Algebra , 8 : 141 – 145 . (preprint early 70's)
   Google Scholar
• Chaiken , S. 1982 . A combinatorial proof of the All Minors Matrix Tree Theorem . SIAM J. Alg. Disc. Meth. , 3 : 319 – 329 .
   Google Scholar
• Faria , I. 1985 . Permanental roots and the star degree of a graph . Linear Algebra Appl. , 64 : 255 – 265 .
   Web of Science ®Google Scholar
• Fiedler , M. 1973 . Algebraic connectivity of graphs . Czechoslovak Math. J. , 23 : 298 – 305 .
   Web of Science ®Google Scholar
• Fiedler , M. 1975 . Eigenvectors of acyclic matrices . Czechoslovak Math. J. , 25 : 607 – 618 .
   Web of Science ®Google Scholar
• Fiedler , M. 1975 . A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory . Czechoslovak Math. J. , 25 : 619 – 633 .
   Web of Science ®Google Scholar
• Grone , R. and Merris , R. 1987 . Algebraic connectivity of trees . Czechoslovak Math. J. , 37 : 660 – 670 .
   Web of Science ®Google Scholar
• Grone , R. and Merris , R. I990 . Coalescence, majorization, edge valuations and the Laplacian spectra of graphs . Linear and Multilinear Algebra , 27 : 139 – 146 .
   Google Scholar
• Grone , R. and Merris , R. 1990 . Ordering trees by algebraic connectivity . Graphs Combin , 6 : 229 – 237 .
   Web of Science ®Google Scholar
• Grone , R. , Merris , R. and Sunder , V. S. 1990 . The Laplacian spectrum of a graph . SIAM J. Matrix Anal Appl. , 11 : 218 – 238 .
   Web of Science ®Google Scholar
• Grone , R. and Zimmermann , G. 1990 . Large eigenvalues of the Laplacian . Linear and Multilinear Algebra , 28 : 45 – 47 .
   Google Scholar
• Kirchhoff , G. 1847 . Über die Auflosung von Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung Galvanischer Strome gefiihrt wird . Ann. Physik Chemie , 72 : 497 – 508 .
   Google Scholar
• Kirkland , S. and Neumann , M. 1997 . Algebraic connectivity of weighted trees under perturbation . Linear and Multilinear Algebra , 42 : 187 – 203 .
   Google Scholar
• Kirkland , S. , Neumann , M. and Shader , B. L. 1996 . Characteristic vertices of weighted trees via Perron values . Linear and Multilinear Algebra , 40 : 311 – 325 .
   Google Scholar
• Kirkland , S. , Neumann , M. and Shader , B. L. 1997 . Distances in weighted trees and group inverses of Laplacian matrices . SIAM J. Matrix Anal. Appl. , 18 : 827 – 841 .
   Web of Science ®Google Scholar
• Lewin , M. 1982 . A generalization of the Matrix-Tree Theorem . Math. Z. , 181 : 55 – 70 .
   Google Scholar
• Merris , R. 1987 . Characteristic vertices of trees . Linear and Multilinear Algebra , 22 : 115 – 131 .
   Google Scholar
• Merris , R. 1989 . An edge version of the Matrix-Tree Theorem and the Wiener Index . Linear and Multilinear Algebra , 25 : 291 – 296 .
   Google Scholar
• Mohar , B. 1988 . The Laplacian spectrum of graphs, Preprint Series Department of Mathematics , Vol. 26 , 353 – 384 . University E. K. Ljubljana .
   Google Scholar
• Mohar , B. 1988 . Laplacian matrices of graphs, Preprint Series Department of Mathematics , Vol. 26 , 385 – 392 . University E. K. Ljubljana .
   Google Scholar
• Poincare , H. 1901 . Second complément à l'analysis situs . Proc. London Math. Soc. , 32 : 277 – 308 .
   Google Scholar