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Öğe BOUNDS FOR LAPLACIAN GRAPH EIGENVALUES(ELEMENT, 2012) Maden, A. Dilek; Buyukkose, SerifeLet G be a connected simple graph whose Laplacian eigenvalues are 0 = mu(n) (G) <= mu(n-1) (G) <= ... <= mu(1) (G). In this paper, we establish some upper and lower bounds for the algebraic connectivity and the largest Laplacian eigenvalue of G.Öğe A Generalization of the Incidence Energy and the Laplacian-Energy-Like Invariant(UNIV KRAGUJEVAC, FAC SCIENCE, 2018) Kaya, Ezgi; Maden, A. DilekFor a graph G and a real number alpha, the graph invariant s(alpha)(G) is the sum of the alpha th powers of the signless Laplacian eigenvalues and sigma(alpha)(G) is the sum of the alpha th powers of the Laplacian eigenvalues of G. In this study, for appropriate vales of alpha, we give some bounds for the generalized versions of incidence energy and of the Laplacian-energy-like invariant of graphs.Öğe MAJORIZATION BOUNDS FOR SIGNLESS LAPLACIAN EIGENVALUES(INT LINEAR ALGEBRA SOC, 2013) Maden, A. Dilek; Cevik, A. SinanIt is known that, for a simple graph G and a real number alpha, the quantity s(alpha)'(G) is defined as the sum of the alpha-th power of non-zero singless Laplacian eigenvalues of G. In this paper, first some majorization bounds over s(alpha)'(G) are presented in terms of the degree sequences, and number of vertices and edges of G. Additionally, a connection between s(alpha)'(G) and the first Zagreb index, in which the Holder's inequality plays a key role, is established. In the last part of the paper, some bounds (included Nordhauss-Gaddum type) for signless Laplacian Estrada index are presented.Öğe Minimality over free monoid presentations(HACETTEPE UNIV, FAC SCI, 2014) Cevik, A. Sinan; Das, Kinkar Ch.; Cangul, I. Naci; Maden, A. DilekAs a continues study of the paper [4], in here, we first state and prove the p-Cockcroft property (or, equivalently, efficiency) for a presentation, say PE, of the semi-direct product of a free abelian monoid rank two by a finite cyclic monoid. Then, in a separate section, we present sufficient conditions on a special case for PE to be minimal whilst it is inefficient.Öğe THE MULTIPLICATIVE ZAGREB COINDICES OF GRAPH OPERATIONS(UTIL MATH PUBL INC, 2017) Nacaroglu, Y.; Maden, A. DilekIn this paper, we present some lower bounds for the first and second multiplicative Zagreb coindices of several graph operations such as union, join, corona product, tensor product, Cartesian product, strong product, lexicographic product in terms of the first and second multiplicative Zagreb coindices and the multiplicative Zagreb indices of their components.Öğe New Bounds on the Incidence Energy, Randic Energy and Randic Estrada Index(UNIV KRAGUJEVAC, FAC SCIENCE, 2015) Maden, A. DilekFor a simple graph G and a real number alpha (not equal 0,1) the graph invariant s(alpha) is equal to the sum of powers of signless Laplacian eigenvalues of G. In this paper, we present some new bounds on s(alpha) of graphs and improve some results which was obtained on bipartite graphs. As a result of these bounds, we also obtain the some improved results on incidence energy. In addition, we study on Randic energy (RE) and Randic Estrada index (REE) of (bipartite) graphs.Öğe New Bounds on the Normalized Laplacian (Randic) Energy(UNIV KRAGUJEVAC, FAC SCIENCE, 2018) Maden, A. DilekIn this paper, we consider the energy of a simple graph with respect to its normalized Laplacian eigenvalues (Randic eigenvalues), which we call the normalized Laplacian energy (also Randic energy). We provide improved upper and lower bounds on these energies for connected (bipartite) graphs.Öğe On Average Eccentricity of Graphs(NATL ACAD SCIENCES INDIA, 2017) Das, Kinkar Ch.; Maden, A. Dilek; Cangul, I. Naci; Cevik, A. SinanThe eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and index.Öğe On the Co-PI Spectral Radius and the Co-PI Energy of Graphs(UNIV KRAGUJEVAC, FAC SCIENCE, 2017) Kaya, Ezgi; Maden, A. DilekThe Co-PI eigenvalues of a connected graph G are the eigenvalues of its Co-PI matrix. In this study, Co-PI energy of a graph is defined as the sum of the absolute values of Co-PI eigenvalues of G. We also give some bounds for the Co-PI spectral radius and the Co-PI energy of graphs.Öğe On the Maximum Clique and the Maximum Independence Numbers of a Graph(AMER INST PHYSICS, 2011) Maden, A. Dilek; Buyukkose, SerifeIn this paper we obtain some bounds for the clique number omega and the independence number alpha, in terms of the eigenvalues of the normalized Laplacian matrix of a graph G.Öğe THE UPPER BOUNDS FOR MULTIPLICATIVE SUM ZAGREB INDEX OF SOME GRAPH OPERATIONS(ELEMENT, 2017) Nacaroglu, Yasar; Maden, A. DilekLet G be a simple graph with vertex set V(G) and edge set E(G). In [7], Eliasi et al. introduced the multiplicative sum Zagreb index of a graph G which is denoted by Pi(*)(1) (G) and is defined by Pi(*)(1)(G) = Pi(uv epsilon V(G)) (d(G)(u) + d(G)(v)) In this paper, we present some upper bounds for the multiplicative sum Zagreb indices of the join, rooted product, corona product, tensor product, Cartesian product, strong product, hierarchical product, lexicographic product of graphs.
