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The new upper bounds on the spectral radius of weighted graphs |
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| Authors: | Sezer Sorgun,?erife Bü yü kkö se |
| Affiliation: | a Nev?ehir University, Department of Mathematics, Nev?ehir, Turkey b Ahi Evran University, Faculty of Sciences and Arts, Department of Mathematics, 40100 K?r?ehir, Turkey |
| Abstract: | Let us consider weighted graphs, where the weights of the edges are positive definite matrices. The eigenvalues of a weighted graph are the eigenvalues of its adjacency matrix and the spectral radius of a weighted graph is also the spectral radius of its adjacency matrix. In this paper, we obtain two upper bounds for the spectral radius of weighted graphs and compare with a known upper bound. We also characterize graphs for which the upper bounds are attained. |
| Keywords: | Weighted graph Adjacency matrix Spectral radius Upper bound |
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