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).