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.
Atıf Kaynağı
Atıf Yapan Yayın
On the Randić incidence energy of graphs
Scopus
Havuzumuzda 3 atıf almış
Let G= (V, E) , V= { v1, v2, … , vn} , be a simple connected graph with n vertices, m edges and vertex degree sequence Δ= d1≥ d2≥ ⋯ ≥ dn= δ> 0 , di= d(vi). Denote by A=(aij)n×n and D= diag (d1, d2, … , dn) , the adjacency and the diagonal degree matrix of G, respectively. The signless Laplacian of G is defined as L+= D+ A, and the normalized signless Laplacian matrix as L+= D- 1 / 2L+D- 1 / 2= I+ D- 1 / 2AD- 1 / 2. The Randić incidence energy of G is defined as IRE(G)=∑i=1nγi+ , where 2=γ1+≥γ2+≥⋯≥γn+≥0, are eigenvalues of L+. Upper and lower bounds on IRE(G) are obtained.
Atıf Yapan Makale Bilgileri
Kurumlar (2)
University of Niš
Nis, Serbia
Yenikent Kardelen Konutları
Konya, Turkey