Yazar "Bozkurt, S. Burcu" seçeneğine göre listele
Listeleniyor 1 - 13 / 13
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe Bounds on the Distance Energy and the Distance Estrada Index of Strongly Quotient Graphs(HINDAWI PUBLISHING CORPORATION, 2013) Bozkurt, S. Burcu; Adiga, Chandrashekara; Bozkurt, DurmusThe notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the distance energy and the distance Estrada index of CSQG whose diameter does not exceed two. Additionally, we show that our results improve most of the results obtained by Gungor and Bozkurt (2009) and Zaferani (2008).Öğe Estimating the Incidence Energy(UNIV KRAGUJEVAC, FAC SCIENCE, 2013) Bozkurt, S. Burcu; Gutman, IvanBounds 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.Öğe On Incidence Energy(UNIV KRAGUJEVAC, FAC SCIENCE, 2014) Bozkurt, S. Burcu; Bozkurt, DurmusThe incidence energy of a graph is defined as the sum of singular values of its incidence matrix. In this paper, we establish some new bounds on the incidence energy of connected graphs.Öğe On Randic energy(ELSEVIER SCIENCE INC, 2014) Gutman, Ivan; Furtula, Boris; Bozkurt, S. BurcuThe 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.Öğe On the complex factorization of the Lucas sequence(PERGAMON-ELSEVIER SCIENCE LTD, 2011) Bozkurt, S. Burcu; Yilmaz, Fatih; Bozkurt, DurmusIn this paper, firstly we present a connection between determinants of tridiagonal matrices and the Lucas sequence. Secondly, we obtain the complex factorization of Lucas sequence by considering how the Lucas sequence can be connected to Chebyshev polynomials by determinants of a sequence of matrices. (C) 2011 Elsevier Ltd. All rights reserved.Öğe ON THE DISTANCE ESTRADA INDEX OF GRAPHS(HACETTEPE UNIV, FAC SCI, 2009) Gungor, A. Dilek; Bozkurt, S. BurcuThe D-eigenval ues mu(1),mu(2)...,mu(n) of a connected graph G are the eigen-values of its distance matrix D. In this paper we define and investigate n the distance Estrada index of the graph G as DEE = DEE(G) = Sigma(n)(i=1) e(mu i) and obtain bounds for DEE(G) and some relation between DEE(G) and the distance energy.Öğe On the Energy and Estrada Index of Strongly Quotient Graphs(Indian Nat Sci Acad, 2012) Bozkurt, S. Burcu; Adiga, Chandrashekara; Bozkurt, DurmuşIn this paper, we consider the strongly quotient graphs and obtain some better results for the energy and Estrada index of these graphs, as well as some relations between Estrada index and the graph energy.Öğe On the normalized Laplacian eigenvalues of graphs(CHARLES BABBAGE RES CTR, 2015) Das, Kinkar Ch.; Gungor, A. Dilek; Bozkurt, S. BurcuLet G = (V, E) be a simple connected graph with n vertices and m edges. Further let lambda(i)(L), i = 1, 2, ..., n, be the non-increasing eigenvalues of the normalized Laplacian matrix of the graph G. In this paper, we obtain the following result: For a connected graph G of order n, lambda(2)(L) = lambda(3)(L) = ... = lambda(n-1)(L) if and only if G is a complete graph K-n or G is a complete bipartite graph K-p,K- q. Moreover, we present lower and upper bounds for the normalized Laplacian spectral radius of a graph and characterize graphs for which the lower or upper bounds is attained.Öğe On the Number of Spanning Trees of Graphs(HINDAWI PUBLISHING CORPORATION, 2014) Bozkurt, S. Burcu; Bozkurt, DurmusWe establish some bounds for the number of spanning trees of connected graphs in terms of the number of vertices (n), the number of edges (m), maximum vertex degree (Delta(1)), minimum vertex degree (delta), first Zagreb index (M-1), and Randic index (R-1).Öğe On the signless Laplacian spectral radius of digraphs(CHARLES BABBAGE RES CTR, 2013) Bozkurt, S. Burcu; Bozkurt, DurmusLet G = (V, E) be a digraph with n vertices and m arcs without loops and multiarcs, V = {v(1), v(2), ... , v(n)}. Denote the outdegree and average 2-outdegree of the vertex v(i) by d(i)(+) and m(i)(+), respectively. Let A (G) be the adjacency matrix and D (G) = diag (d(1)(+), d(2)(+), ... , d(n)(+)) be the diagonal matrix with outdegree of the vertices of the digraph G. Then we call Q (G) = D (G) + A (G) signless Laplacian matrix of G. In this paper, we obtain some upper and lower bounds for the spectral radius of Q (G) which is called signless Laplacian spectral radius of G. We also show that some bounds involving outdegrees and the average 2-outdegrees of the vertices of G can be obtained from our bounds.Öğe On the spectral radius and the energy of a digraph(TAYLOR & FRANCIS LTD, 2015) Bozkurt, S. Burcu; Bozkurt, Durmus; Zhang, Xiao-DongThe energy of a digraph D is defined as E (D) = Sigma(n)(i=1) vertical bar Re (z(i))vertical bar, where z(1), ... , z(n) are the (possibly complex) eigenvalues of D. In this paper, we obtain an improved lower bound on the spectral radius of D. Considering this result, we present an upper bound on the energy of D. We also show that our results generalize and improve some known results for graphs and digraphs.Öğe On the Sum of Powers of Normalized Laplacian Eigenvalues of Graphs(Univ Kragujevac, Fac Science, 2012) Bozkurt, S. Burcu; Bozkurt, DurmuşFor a graph G without isolated vertices and a real alpha not equal 0, we introduce a new graph invariant s(alpha)(*) (G)- the sum of the alpha th power of the non-zero normalized Laplacian eigenvalues of G. Recently, the cases alpha = 2 and -1 have appeared in various problems in the literature. Here, we present some lower and upper bounds of s(alpha)(*)(G) for a connected graph G, where alpha not equal 0, 1. We also discuss the case alpha = -1.Öğe Randic energy and Randic estrada index of a graph(2012) Bozkurt, S. Burcu; Bozkurt, DurmusLet G be a simple connected graph with n vertices and let di be the degree of its i-th vertex. The Randi´c matrix of G is the square matrix of order n whose (i,j)-entry is equal to 1/ \sqrt{d_id_j} if the i-th and j-th vertex of G are adjacent, and zero otherwise. The Randi´c eigenvalues are the eigenvalues of the Randi´c matrix. The Randi´c energy is the sum of the absolute values of the Randi´c eigenvalues. In this paper, we introduce a new index of the graph G which is called Randi´c Estrada index. In addition, we obtain lower and upper bounds for the Randi´c energy and the Randi´c Estrada index of G. 2000 Mathematics Subject Classifications: 05C50,15A18
