Yazar "Gutman, Ivan" seçeneğine göre listele

Listeleniyor 1 - 9 / 9
  • Küçük Resim Yok
    Öğe
    Bounds for Resistance-Distance Spectral Radius
    (HACETTEPE UNIV, FAC SCI, 2013) Maden, A. Dilek Gungor; Gutman, Ivan; Cevik, A. Sinan
    Lower and upper bounds as well as Nordhauss-Gaddum-type results for the resistance-distance spectral radius are obtained.
  • Küçük Resim
    Öğe
    Derived Graphs of Some Graphs
    (2012) Jog, R. Jog; Satısh, P. Hande; Gutman, Ivan; Bozkurt, Ş. Burcu
    The derived graph of a simple graph G, denoted by G†, is the graph having the same vertex set as G, in which two vertices are adjacent if and only if their distance in G is two. Continuing the studies communicated in Kragujevac J. Math. 34 (2010), 139-146, we examined derived graphs of some graphs and determine their spectra.
  • Küçük Resim Yok
    Öğe
    Estimating the Incidence Energy
    (UNIV KRAGUJEVAC, FAC SCIENCE, 2013) Bozkurt, S. Burcu; Gutman, Ivan
    Bounds for the incidence energy of connected bipartite graphs were recently reported. We now extend these results to connected non-bipartite graphs. In addition, these bounds are generalized so as to apply to the sum of alpha-th powers of signless Laplacian eigenvalues, for any real alpha.
  • Küçük Resim Yok
    Öğe
    Inverse Problem for Sigma Index
    (UNIV KRAGUJEVAC, FAC SCIENCE, 2018) Gutman, Ivan; Togan, Muge; Yurttas, Aysun; Cevik, Ahmet Sinan; Cangul, Ismail Naci
    If G is a (molecular) graph and d(v), the degree of its vertex u, then its sigma index is defined as sigma(G) = Sigma(d(u) - d(v))(2), with summation going over all pairs of adjacent vertices. Some basic properties of sigma(G) are established. The inverse problem for topological indices is about the existence of a graph having its index value equal to a given non-negative integer. We study the problem for the sigma index and first show that sigma(G) is an even integer. Then we construct graph classes in which sigma(G) covers all positive even integers. We also study the inverse problem for acyclic, unicyclic, and bicyclic graphs.
  • Küçük Resim Yok
    Öğe
    On Laplacian Energy
    (UNIV KRAGUJEVAC, FAC SCIENCE, 2013) Das, Kinkar Ch.; Gutman, Ivan; Cevik, A. Sinan; Zhou, Bo
    Let G be a connected graph of order n with Laplacian eigenvalues mu(1) >= mu(2) >= ... >= mu(n-1) > mu(n) = 0. The Laplacian energy of the graph G is defined as LE = LE(G) = (n)Sigma(i=1)vertical bar mu(i)-2m/n vertical bar. Upper bounds for LE are obtained, in terms of n and the number of edges m.
  • Küçük Resim Yok
    Öğe
    On Randic energy
    (ELSEVIER SCIENCE INC, 2014) Gutman, Ivan; Furtula, Boris; Bozkurt, S. Burcu
    The Randic matrix R = (r(ij)) of a graph G whose vertex vi has degree d(i) is defined by r(ij) = 1/root d(i)d(j) if the vertices v(i) and v(j) are adjacent and r(ij) = 0 otherwise. The Randic. energy RE is the sum of absolute values of the eigenvalues of R. RE coincides with the normalized Laplacian energy and the normalized signless-Laplacian energy. Several properties or R and RE are determined, including characterization of graphs with minimal RE. The structure of the graphs with maximal RE is conjectured. (C) 2013 Elsevier Inc. All rights reserved.
  • Küçük Resim Yok
    Öğe
    On the Laplacian-energy-like invariant
    (ELSEVIER SCIENCE INC, 2014) Das, Kinkar Ch.; Gutman, Ivan; Cevik, A. Sinan
    Let G be a connected graph of order n with Laplacian eigenvalues mu(1) >= mu(2) >= ... mu(n-1) >mu(n) = 0. The Laplacian-energy-like invariant of the graph G is defined as LEL = LEL(G) = Sigma(n-1)(i=1)root mu(i) . Lower and upper bounds for LEL are obtained, in terms of n, number of edges, maximum vertex degree, and number of spanning trees. (C) 2013 Elsevier Inc. All rights reserved.
  • Küçük Resim
    Öğe
    Randic Matrix and Randic Energy
    (Univ Kragujevac, Fac Science, 2010) Bozkurt, Ş. Burcu; Güngör, A. Dilek; Gutman, Ivan; Çevik, A. Sinan
    If G is a graph on n vertices, and d(i) is the degree of its i-th vertex, then the Randic matrix of G is the square matrix of order n whose (i, j)-entry is equal to 1/root d(i) d(j) di 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 Randic index, the Randic matrix seems to have not been much studied in mathematical chemistry. In this paper we define the Randic energy as the sum of the absolute values of the eigenvalues of the Randic matrix, and establish mine of its properties, in particular lower and upper bounds for it.
  • Küçük Resim Yok
    Öğe
    Randic Spectral Radius and Randic Energy
    (Univ Kragujevac, Fac Science, 2010) Bozkurt, Ş. Burcu; Güngör, A. Dilek; Gutman, Ivan
    Let G be a simple connected graph with n vertices and let d(i) be the degree of its i-th vertex. The Randic matrix of G is the square matrix of order n whose (i, j)-entry is equal to 1/root d(i)d(j) di if the i-th and j-th vertex of G are adjacent, and zero otherwise. The Randic eigenvalues are the eigenvalues of the Rancho matrix. The greatest Randic eigenvalue is the Randic spectral radius of C. The Randic energy is the sum of the absolute values of the Randic eigenvalues. Lower bounds for Randic spectral radius and an upper bound for Randic energy are obtained. Graphs for which these bounds are best possible are characterized.