AN UPPER BOUND ON THE SPECTRAL RADIUS OF WEIGHTED GRAPHS

Sorgun S., Buyukkose S., ÖZARSLAN H.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.42, no.5, pp.517-524, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 5
  • Publication Date: 2013
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.517-524
  • Erciyes University Affiliated: Yes

Abstract

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain another upper bound which is sharp on the spectral radius of the adjacency matrix and compare with some known upper bounds with the help of some examples of graphs. We also characterize graphs for which the bound is attained.