Graphs and Hermitian matrices: Eigenvalue interlacing

Discrete Mathematics

Volumn 289, Issue 1-3, 2004, Pages 119-127

  Bollobás, Béla ^a,b   Nikiforov, Vladimir ^a  

^a University of Memphis   (United States)

^b TRINITY COLLEGE   (United Kingdom)

Author keywords

Graph eigenvalues; Interlacing; Partitioned matrix; Second eigenvalue; Smallest eigenvalue

Indexed keywords

BLOCK CODES; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING; THEOREM PROVING;

GRAPH EIGENVALUES; INTERLACING; PARTITIONED MATRIX; SECOND EIGENVALUE; SMALLEST EIGENVALUE;

GRAPH THEORY;

EID: 10444219620     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2004.07.011     Document Type: Article

References (13)

1. N. Aronszajn, Rayleigh-Ritz and A. Weinstein methods for approximation of eigenvalues. I. Operators in a Hubert space, Proc. Nat. Acad. Sci. USA 34 (1948) 474-480.
2. R. Bhatia, Matrix Analysis, Graduate Texts in Mathematics, vol. 165, Springer, New York, 1997.
3. B. Bollobás, Modern Graph Theory, Graduate Texts in Mathematics, vol. 184, Springer, New York, 1998.
4. F.R.K. Chung, R.L. Graham, R.M. Wilson, Quasi-random graphs, Combinatorica 9 (1989) 345-362.
5. R. Courant, D. Hilbert, Methoden der Mathematischen Physik, vol. 1, springer, Berlin, 1924.
6. M.A. Fiol, Eigenvalue interlacing and weight parameters of graphs, Linear Algebra Appl. 290 (1999) 275-301.
7. W.H. Haemers, Eigenvalue methods, in: A. Schrijver (Ed.), Packing and Covering in Combinatorics, Mathematical Centre Tracts, vol. 106, Mathematical Centre, Amsterdam, 1979, pp. 15-38.
8. W.H. Haemers, Eigenvalue Techniques in Design and Graph Theory, Mathematical Centre Tracts, vol. 121, Mathematical Centre, Amsterdam, 1980.
9. W.H. Haemers, Interlacing eigenvalues and graphs, Linear Algebra Appl. 226/228 (1995) 593-616.
10. A. J. Hoffman, On eigenvalues and colourings of graphs, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, 1970, pp. 79-91.
11. R. Horn, C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
12. B. Mohar, Some applications of Laplace eigenvalues of graphs, Graph Symmetry, Montreal PQ, 1996 NATO Advanced Science Institute Series C: Mathematical and Physical Sciences, vol. 497, Kluwer Academic Publishers, Dordrecht, 1997, pp. 225-275.
13. V. Nikiforov, On the edge distribution of a graph, Combin. Probab. Comput. 10 (2001) 543-555.