HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.42, sa.5, ss.517-524, 2013 (SCI-Expanded)
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.