Skip to main content
SpringerLink
Log in

Bounds for the Least Laplacian Eigenvalue of a Signed Graph

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fiedler, M.: Algebraic connectivity of graphs. Czechoslovak Math. J., 23(1), 298–305 (1973)

    MathSciNet  Google Scholar 

  2. Merris, R.: Laplacian Matrices of Graphs: A Survey. Linear Algebra and its Applications, 197/198(1), 143–176 (1994)

    Article  MathSciNet  Google Scholar 

  3. Mohar, B.: Some applications of Laplacian eigenvalues of graphs, Graph Symmetry (G. Hahn and G. Sabidussi, eds.), Kluwer Academic Publishers, Boston, 225–275, 1997

  4. Chung, F. R.: Spectral Graph Theory, CBMS Lecture Notes, AMS Publication, 1997

  5. Harary, F.: On the notion of balanced in a signed graph. Michigan Math. J., 2(1), 143–146 (1953)

    Article  MathSciNet  Google Scholar 

  6. Deradass, B., Archarya, L.: Spectral criterion for cycle balance in networks. J. of Graph Theory, 4(1), 1–11 (1980)

    Google Scholar 

  7. Zaslavsky, T.: Signed graphs. Discrete Appl. Math., 4(1), 47–74 (1982)

    Article  MathSciNet  Google Scholar 

  8. Chaiken, S.: A combinatorial proof of the all minors matrix tree theorem. SIAM J. Algebraic Discrete Methods, 3(2), 319–329 (1982)

    MathSciNet  Google Scholar 

  9. Cameron, P. J., Seidel, J., Tsaranov, J. J.: Signed graphs, root lattices, and Coxeter groups. J. of Algebra, 164(1), 173–209 (1994)

    Article  MathSciNet  Google Scholar 

  10. Hou, Y. P., Li, J. S.: On the Laplacian eigenvalues of signed graphs. Linear and Mutilinear Algebra, 51(1), 21–30 (2003)

    Article  Google Scholar 

  11. Desai, B., Rao, V.: A characterization of the smallest eigenvalue of a graph. J. of Graph Theory, 18(2), 181–194 (1994)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, Changsha 410081, P. R. China

    Yao Ping Hou

Authors
  1. Yao Ping Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yao Ping Hou.

Additional information

The project is supported by the NSF of China (No. 19971086) and SRP (No. 03B019) from the Education Committee of Hunan Province

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hou, Y.P. Bounds for the Least Laplacian Eigenvalue of a Signed Graph. Acta Math Sinica 21, 955–960 (2005). https://doi.org/10.1007/s10114-004-0437-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-004-0437-9

Keywords

MR (2000) Subject Classification

Search

Navigation