Kurumun Atıf Alan Makalesi
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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
On the signless Laplacian and normalized signless Laplacian spreads of graphs
Scopus
Havuzumuzda 1 atıf almış
Let G = (V, E), V = {v1, v2, …, vn}, be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≽ d2 ≽ … ≽ dn. Denote by A and D the adjacency matrix and diagonal vertex degree matrix of G, respectively. The signless Laplacian of G is defined as L+ = D + A and the normalized signless Laplacian matrix as r(G)=γ2+/γn+. The normalized signless Laplacian spreads of a connected nonbipartite graph G are defined as l(G)=γ2+−γn+, where γ1+⩾γ2+⩾..⩾γn+⩾0 are eigenvalues of ℒ+. We establish sharp lower and upper bounds for the normalized signless Laplacian spreads of connected graphs. In addition, we present a better lower bound on the signless Laplacian spread.
Atıf Yapan Makale Bilgileri
Kurumlar (2)
Karamanoğlu Mehmetbey Üniversitesi
Karaman, Turkey
University of Niš
Nis, Serbia