Sezer Sorgun

The new upper bounds on the spectral radius of weighted graphs

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.

On the bounds for the largest Laplacian eigenvalues of weighted graphs

Abstract We consider weighted graphs, such as graphs where the edge weights are positive definite matrices. The Laplacian eigenvalues of a graph are the eigenvalues of the Laplacian matrix of a graph G . We obtain an upper bound for the largest Laplacian eigenvalue and we compare this bound with previously known bounds.

The kite graph is determined by its adjacency spectrum

The kite graph is obtained by appending the complete graph with p vertices to a pendant vertex of the path graph with q vertices. In this paper, we prove that the kite graph is determined by its adjacency spectrum for all p and q.

Graf Matrisleri ve Çarpım Matrisinin En Büyük Öz Değerleri Arasında Bazı Bağıntılar

( ) ve ( ) sirasiyla bir grafinin komsuluk matrisi ve nokta derecelerinin bir kosegen matrisi olmak uzere ( ) ( ) ( ) matrisini tanimlariz. Bu makalede bu carpim matrisinin spektral yaricapi ile graf matrislerinin en buyuk oz degerleri arasinda bazi bagintilar elde edilmistir. Ayrica numerik sonuclar da verilmistir