Kurumun Atıf Alan Makalesi
Atıf Alan Yayın
Randic matrix and randić energy
Scopus
Toplam 156 atıf
If G is a graph on n vertices, and di, is the degree of its i-th vertex, then the Randiá matrix of G is the square matrix of order n whose (i, j)-entry is equal to √didi if the i-th and j-th vertex of G are adjacent, and zero otherwise. This matrix in a natural way occurs within Laplacian spectral theory, and provides the non-trivial part of the so-called normalized Laplacian matrix. In spite of its obvious relation to the famous Randić index, the Randić matrix seems to have not been much studied in mathematical chemistry. In this paper we define the Randić energy as the sum of the absolute values of the eigenvalues of the Randić matrix, and establish some of its properties, in particular lower and upper bounds for it.
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Atıf Yapan Yayın
Some new bounds for the sum of powers of the normalized Laplacian eigenvalues of graphs
Scopus
Havuzumuzda Open Access
Let G = (V, E) be a simple connected graph of order n ≥ 2, size m with normalized Laplacian eigenvalues γ1 ≥ γ2 ≥ · · · ≥ γn−1 > γn = 0. Denote with (Formula Presented), where α is an arbitrary real number, the sum of powers of normalized Laplacian eigenvalues of graphs. In this paper several inequalities involving invariants of the form sα(G), for various real α are proved. Our results not only generalize and improve some previous results on sα (G), Kemeny constant and Laplacian incidence energy, but also present new bounds for these graph invariants.
Atıf Yapan Makale Bilgileri
Kurumlar (2)
Selçuk Üniversitesi
Selçuklu, Turkey
University of Niš
Nis, Serbia