Tatjana Aleksic | University of Kragujevac (original) (raw)

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Papers by Tatjana Aleksic

Research paper thumbnail of More on "Connected (n, m)-graphs with minimum and maximum zeroth-order general Randic index

Discrete Applied Mathematics, 2009

Let G be a graph and d(u) denote the degree of a vertex u in G. The zeroth-order general

Research paper thumbnail of Bicyclic graphs for which the least eigenvalue is minimum

Linear Algebra and Its Applications, 2009

The spread of a graph is defined to be the difference between the greatest eigenvalue and the lea... more The spread of a graph is defined to be the difference between the greatest eigenvalue and the least eigenvalue of the adjacency matrix of the graph. In this paper we determine the unique graph with minimum least eigenvalue among all connected bicyclic graphs of order n. Also, we determine the unique graph with maximum spread in this class for each n 28.

Research paper thumbnail of On the least eigenvalue of cacti

Linear Algebra and Its Applications, 2011

Among the cacti with n vertices and k cycles we determine a unique cactus whose least eigenvalue ... more Among the cacti with n vertices and k cycles we determine a unique cactus whose least eigenvalue is minimal. We also explore cacti with n vertices and among them, we find a unique cactus whose least eigenvalue is minimal.

Research paper thumbnail of Further results on the least eigenvalue of connected graphs

Linear Algebra and Its Applications, 2011

In this paper, we identify within connected graphs of order n and size n+k (with 0⩽k⩽4 and n⩾k+5)... more In this paper, we identify within connected graphs of order n and size n+k (with 0⩽k⩽4 and n⩾k+5) the graphs whose least eigenvalue is minimal. It is also observed that the same graphs have the largest spectral spread if n is large enough.

Research paper thumbnail of Ihara Coefficients: A Flexible Tool for Higher Order Learning

The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs f... more The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we propose a novel hypergraph characterization method by using the Ihara coefficients, i.e. the characteristic polynomial coefficients extracted from the Ihara zeta function. We investigate the flexibility of the Ihara coefficients for learning relational structures with different relational orders. Furthermore, we introduce an efficient method for computing the coefficients. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity in the hypergraph Laplacian. In experiments we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian.

Research paper thumbnail of Hypergraphs, Characteristic Polynomials and the Ihara Zeta Function

In this paper we make a characteristic polynomial analysis on hypergraphs for the purpose of clus... more In this paper we make a characteristic polynomial analysis on hypergraphs for the purpose of clustering. Our starting point is the Ihara zeta function [8] which captures the cycle structure for hypergraphs. The Ihara zeta function for a hypergraph can be expressed in a determinant form as the reciprocal of the characteristic polynomial of the adjacency matrix for a transformed graph representation. Our hypergraph characterization is based on the coefficients of the characteristic polynomial, and can be used to construct feature vectors for hypergraphs. In the experimental evaluation, we demonstrate the effectiveness of the proposed characterization for clustering hypergraphs.

Research paper thumbnail of Quantum walks, Ihara zeta functions and cospectrality in regular graphs

Quantum Information Processing, 2011

In this paper we explore an interesting relationship between discrete-time quantum walks and the ... more In this paper we explore an interesting relationship between discrete-time quantum walks and the Ihara zeta function of a graph. The paper commences by reviewing the related literature on the discrete-time quantum walks and the Ihara zeta function. Mathematical definitions of the two concepts are then provided, followed by analyzing the relationship between them. Based on this analysis we are able to account for why the Ihara zeta function can not distinguish cospectral regular graphs. This analysis suggests a means by which to develop zeta functions that have potential in distinguishing such structures.

Research paper thumbnail of A polynomial characterization of hypergraphs using the Ihara zeta function

Pattern Recognition, 2011

The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs f... more The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we develop a polynomial characterization for hypergraphs based on the Ihara zeta function. We investigate the flexibility of the polynomial coefficients for learning relational structures with different relational orders. Furthermore, we develop an efficient method for computing the coefficient set. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity if the hypergraph Laplacian is used. In our experimental evaluation, we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian.

Research paper thumbnail of More on "Connected (n, m)-graphs with minimum and maximum zeroth-order general Randic index

Discrete Applied Mathematics, 2009

Let G be a graph and d(u) denote the degree of a vertex u in G. The zeroth-order general

Research paper thumbnail of Bicyclic graphs for which the least eigenvalue is minimum

Linear Algebra and Its Applications, 2009

The spread of a graph is defined to be the difference between the greatest eigenvalue and the lea... more The spread of a graph is defined to be the difference between the greatest eigenvalue and the least eigenvalue of the adjacency matrix of the graph. In this paper we determine the unique graph with minimum least eigenvalue among all connected bicyclic graphs of order n. Also, we determine the unique graph with maximum spread in this class for each n 28.

Research paper thumbnail of On the least eigenvalue of cacti

Linear Algebra and Its Applications, 2011

Among the cacti with n vertices and k cycles we determine a unique cactus whose least eigenvalue ... more Among the cacti with n vertices and k cycles we determine a unique cactus whose least eigenvalue is minimal. We also explore cacti with n vertices and among them, we find a unique cactus whose least eigenvalue is minimal.

Research paper thumbnail of Further results on the least eigenvalue of connected graphs

Linear Algebra and Its Applications, 2011

In this paper, we identify within connected graphs of order n and size n+k (with 0⩽k⩽4 and n⩾k+5)... more In this paper, we identify within connected graphs of order n and size n+k (with 0⩽k⩽4 and n⩾k+5) the graphs whose least eigenvalue is minimal. It is also observed that the same graphs have the largest spectral spread if n is large enough.

Research paper thumbnail of Ihara Coefficients: A Flexible Tool for Higher Order Learning

The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs f... more The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we propose a novel hypergraph characterization method by using the Ihara coefficients, i.e. the characteristic polynomial coefficients extracted from the Ihara zeta function. We investigate the flexibility of the Ihara coefficients for learning relational structures with different relational orders. Furthermore, we introduce an efficient method for computing the coefficients. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity in the hypergraph Laplacian. In experiments we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian.

Research paper thumbnail of Hypergraphs, Characteristic Polynomials and the Ihara Zeta Function

In this paper we make a characteristic polynomial analysis on hypergraphs for the purpose of clus... more In this paper we make a characteristic polynomial analysis on hypergraphs for the purpose of clustering. Our starting point is the Ihara zeta function [8] which captures the cycle structure for hypergraphs. The Ihara zeta function for a hypergraph can be expressed in a determinant form as the reciprocal of the characteristic polynomial of the adjacency matrix for a transformed graph representation. Our hypergraph characterization is based on the coefficients of the characteristic polynomial, and can be used to construct feature vectors for hypergraphs. In the experimental evaluation, we demonstrate the effectiveness of the proposed characterization for clustering hypergraphs.

Research paper thumbnail of Quantum walks, Ihara zeta functions and cospectrality in regular graphs

Quantum Information Processing, 2011

In this paper we explore an interesting relationship between discrete-time quantum walks and the ... more In this paper we explore an interesting relationship between discrete-time quantum walks and the Ihara zeta function of a graph. The paper commences by reviewing the related literature on the discrete-time quantum walks and the Ihara zeta function. Mathematical definitions of the two concepts are then provided, followed by analyzing the relationship between them. Based on this analysis we are able to account for why the Ihara zeta function can not distinguish cospectral regular graphs. This analysis suggests a means by which to develop zeta functions that have potential in distinguishing such structures.

Research paper thumbnail of A polynomial characterization of hypergraphs using the Ihara zeta function

Pattern Recognition, 2011

The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs f... more The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we develop a polynomial characterization for hypergraphs based on the Ihara zeta function. We investigate the flexibility of the polynomial coefficients for learning relational structures with different relational orders. Furthermore, we develop an efficient method for computing the coefficient set. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity if the hypergraph Laplacian is used. In our experimental evaluation, we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian.