BibTex RIS Cite

A Bound On The Spectral Radius of A Weighted Graph

Year 2009, Volume: 22 Issue: 4, 263 - 266, 30.03.2010

Şerife Büyükköse Sezer Sorgun

Abstract

Let

 

G be simple, connected weighted graphs, where the edge weights are positive definite matrices. In this paper, we will ive an upper bound on the spectral radius of the adjacency matrix for a graph G and characterize graphs for which the bound is attained.

Keywords

Weighted graph; Adjacency matrix; Spectral radius; Upper bound

References

  • Berman, A., Zhang, X.D., “On the spectral radius of graphs with cut vertices”, J. Combin. Theory Ser. B, 83: 233-240 (2001).
  • Das, K.C., Bapat, R.B., “A sharp bound on the spectral radius of weighted graphs”, Discrete Math., 308 (15): 3180-3186 (2008).
  • Horn, R., Johnson, C., R., “Matrix Analysis”, Cambridge University Press, New York, 1980.
  • Brualdi, R.A., Hoffman, A.J., “On the spectral radius of a (0,1) matrix”, Linear Algebra Appl., 65: 133-146 (1985).
  • Cvetkovic, D., Rowlinson, P., “The largest eigenvalue of a graph: a survey”, Linear Multilinear Algebra, 28: 3-33 (1990).
  • Hong, Y., “Bounds of eigenvalues of graphs”, Discrete Math., 123: 65-74 (1993).
  • Stanley, R.P., “A bound on the spectral radius of graphs with e edges”, Linear Algebra Appl., 67: 267-269 (1987).

Year 2009, Volume: 22 Issue: 4, 263 - 266, 30.03.2010

Şerife Büyükköse Sezer Sorgun

Abstract

References

  • Berman, A., Zhang, X.D., “On the spectral radius of graphs with cut vertices”, J. Combin. Theory Ser. B, 83: 233-240 (2001).
  • Das, K.C., Bapat, R.B., “A sharp bound on the spectral radius of weighted graphs”, Discrete Math., 308 (15): 3180-3186 (2008).
  • Horn, R., Johnson, C., R., “Matrix Analysis”, Cambridge University Press, New York, 1980.
  • Brualdi, R.A., Hoffman, A.J., “On the spectral radius of a (0,1) matrix”, Linear Algebra Appl., 65: 133-146 (1985).
  • Cvetkovic, D., Rowlinson, P., “The largest eigenvalue of a graph: a survey”, Linear Multilinear Algebra, 28: 3-33 (1990).
  • Hong, Y., “Bounds of eigenvalues of graphs”, Discrete Math., 123: 65-74 (1993).
  • Stanley, R.P., “A bound on the spectral radius of graphs with e edges”, Linear Algebra Appl., 67: 267-269 (1987).
There are 7 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Şerife Büyükköse This is me

Sezer Sorgun

Publication Date March 30, 2010
Published in Issue Year 2009 Volume: 22 Issue: 4

Cite

APA Büyükköse, Ş., & Sorgun, S. (2010). A Bound On The Spectral Radius of A Weighted Graph. Gazi University Journal of Science, 22(4), 263-266.
AMA Büyükköse Ş, Sorgun S. A Bound On The Spectral Radius of A Weighted Graph. Gazi University Journal of Science. March 2010;22(4):263-266.
Chicago Büyükköse, Şerife, and Sezer Sorgun. “A Bound On The Spectral Radius of A Weighted Graph”. Gazi University Journal of Science 22, no. 4 (March 2010): 263-66.
EndNote Büyükköse Ş, Sorgun S (March 1, 2010) A Bound On The Spectral Radius of A Weighted Graph. Gazi University Journal of Science 22 4 263–266.
IEEE Ş. Büyükköse and S. Sorgun, “A Bound On The Spectral Radius of A Weighted Graph”, Gazi University Journal of Science, vol. 22, no. 4, pp. 263–266, 2010.
ISNAD Büyükköse, Şerife - Sorgun, Sezer. “A Bound On The Spectral Radius of A Weighted Graph”. Gazi University Journal of Science 22/4 (March 2010), 263-266.
JAMA Büyükköse Ş, Sorgun S. A Bound On The Spectral Radius of A Weighted Graph. Gazi University Journal of Science. 2010;22:263–266.
MLA Büyükköse, Şerife and Sezer Sorgun. “A Bound On The Spectral Radius of A Weighted Graph”. Gazi University Journal of Science, vol. 22, no. 4, 2010, pp. 263-6.
Vancouver Büyükköse Ş, Sorgun S. A Bound On The Spectral Radius of A Weighted Graph. Gazi University Journal of Science. 2010;22(4):263-6.