AN UPPER BOUND ON THE SPECTRAL RADIUS OF WEIGHTED GRAPHS

Abstract

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

Keywords

• Weighted graph
• Adjacency matrix
• Spectral radius
• Upper bound

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