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The independence fractal of a graph

J.I. Brown, C.A. Hickman, R.J. Nowakowski
2003 Journal of combinatorial theory. Series B (Print)  
We prove that in fact they converge (in the Hausdorff topology) to the Julia set of the independence polynomial of G; thereby associating with G a fractal.  ...  We ask here: for higher products of a graph G with itself, where are the roots of their independence polynomials approaching?  ...  Independence fractals of graphs: a general theory We set out now to describe just where the reduced independence roots of powers G k (i.e., the roots of f G k ¼ f G 1 k ) of a graph G are approaching as  ... 
doi:10.1016/s0095-8956(02)00014-x fatcat:7esq4zbqvzaizeged4sdfufj6a

Independence roots and independence fractals of certain graphs

Saeid Alikhani, Yee-hock Peng
2010 Journal of Applied Mathematics and Computing  
The independence polynomial of a graph G is the polynomial I(G, x) = i k x k , where i k denote the number of independent sets of cardinality k in G.  ...  Graph theory and geometrical fractal are two examples of branches of mathematics which have applications in architecture and design.  ...  An independent set of a graph G is a set of vertices where no two vertices are adjacent. The independence number is the size of a maximum independent set in the graph.  ... 
doi:10.1007/s12190-010-0389-4 fatcat:64dbmk2yczeedhkol7q3qf3bzm

A NOVEL APPROACH FOR PATTERN RECOGNITION BY USING NETWORK AND THEORY OF COMPLEXITY

Matej Babič
2018 Journal of Production Engineering  
Intelligent systems are a new wave of the embedded and real-time systems that are highly connected, with a massive processing power and performing complex applications.  ...  We use a method which combines an intelligent genetic algorithm and multiple regression to predict all closeness centralization of network created with connection maximum value of 3D graph of hardened  ...  A regression model relates Y to a function of X and β. Y=(X, β), where the unknown parameters, denoted as β, which may represent a scalar or a vector. The independent variables, X.  ... 
doi:10.24867/jpe-2018-01-021 fatcat:ee5jl2vtnvejpdz7l6wqgah3tm

Some Combinatorial Problems in Power-Law Graphs

Che Jiang, Wanyue Xu, Xiaotian Zhou, Zhongzhi Zhang, Haibin Kan
2021 Computer journal  
For both graphs, we determine exactly or recursively their matching number, independence number, domination number, the number of maximum matchings, the number of maximum independent sets and the number  ...  The power-law behavior is ubiquitous in a majority of real-world networks, and it was shown to have a strong effect on various combinatorial, structural and dynamical properties of graphs.  ...  DATA AVAILABILITY STATEMENT No new data were generated or analysed in support of this research.  ... 
doi:10.1093/comjnl/bxab007 fatcat:xtcxwvqzlrc5boq2d2on2glebm

The duality of fractals: roughness and self-similarity

Nicolas Bez, Sophie Bertrand
2010 Theoretical Ecology  
The fractal dimension (D HB ) is an interesting metrics because it is supposed to quantify by a single value, scale independence and roughness of ecological objects.  ...  The paper concludes on a synthesis of practical recommendations to ecologists when using fractal dimension.  ...  Matheron for the seminar on fractals he gave in the early 1990s. These slides were of particular use for us whilst working on this subject.  ... 
doi:10.1007/s12080-010-0084-y fatcat:b4crrta66zconkp7fckc2kaoka

The k-fractal of a simplicial complex

J.I. Brown, C.A. Hickman, R.J. Nowakowski
2004 Discrete Mathematics  
We prove that they converge to the Julia set of k C (x), thereby associating with C a fractal.  ...  The k-polynomial of a simplicial complex C is the function k C (x) = i¿1 fix i where fi is the number of i-faces in C.  ...  The collection of all independent sets of a graph G also forms a simplicial complex over V (G)-the independence complex of G-whose dimension is precisely the independence number of G.  ... 
doi:10.1016/j.disc.2003.12.014 fatcat:5mxaytz5r5gx7njcb47zif537a

AN ANALYSIS OF STABILITY OF TRENDS IN MUTUAL FUNDS USING FRACTAL DIMENSION INDEX (FDI) COMPUTED FROM HURST EXPONENTS

Priyadarshini E, Chandra Babu A
2010 International Journal on Information Sciences and Computing  
The fractal dimension index (FDI) is a specialized tool that applies the principles of chaos theory and fractals.  ...  Chaos is a nonlinear, dynamic system that appears to be random but is actually a higher form of order. All chaotic systems have a quantifying measurement known as a fractal dimension.  ...  If the process is an independent random process, then the plot of V versus Log n will be flat.  ... 
doi:10.18000/ijisac.50076 fatcat:wphjuqlgifa2zig52i6yil7n74

Phase ordering and universality for continuous symmetry models on graphs

R Burioni, F Corberi, A Vezzani
2009 Journal of Statistical Mechanics: Theory and Experiment  
We study the phase-ordering kinetics following a temperature quench of O(N) continuous symmetry models with and 4 on graphs.  ...  The exponent a for the integrated response function and the exponent z, describing the growing length, are related to the large scale topology of the networks through the spectral dimension and the fractal  ...  (i, j) and i.e. the spectral and fractal dimensions of the product graph are the sum of the dimensions of the original graphs.  ... 
doi:10.1088/1742-5468/2009/02/p02040 fatcat:pihlvgndijarhio4jgzxexivnq

DESIGN AND SIMULATION OF SIERPINSKI CARPET FRACTAL ANTENNA AND COMPARISION OF DIFFERENT FEEDS

S.Ravi .
2014 International Journal of Research in Engineering and Technology  
In this paper, a multi band microstrip antenna is designed by applying fractal concept to a rectangular microstrip antenna.  ...  The rapid growth in wireless communication has led to need of antennas with increased bandwidth, high gain and low profile.  ...  Fractals are self-similar structures and independent of scale [3] . The fractal term was coined in 1975 by, Benoit B. Mandelbrot who is a French mathematician.  ... 
doi:10.15623/ijret.2014.0316007 fatcat:pmbh24dzi5a2jdywzp4x6cqc6u

Next Generation Data Mining Tools: Power Laws and Self-similarity for Graphs, Streams and Traditional Data [chapter]

Christos Faloutsos
2003 Lecture Notes in Computer Science  
How about the distributions of galaxies in the sky, or the distribution of a company's customers in geographical space?  ...  What patterns can we find in a bursty web traffic? On the web or internet graph itself?  ...  We show that the theory of fractals provide powerful tools to solve the above problems. Definitions Intuitively, a set of points is a fractal if it exhibits self-similarity over all scales.  ... 
doi:10.1007/978-3-540-39857-8_3 fatcat:oxs62jcyp5huzjzbikx2szn2ki

Next Generation Data Mining Tools: Power Laws and Self-similarity for Graphs, Streams and Traditional Data [chapter]

Christos Faloutsos
2003 Lecture Notes in Computer Science  
How about the distributions of galaxies in the sky, or the distribution of a company's customers in geographical space?  ...  What patterns can we find in a bursty web traffic? On the web or internet graph itself?  ...  We show that the theory of fractals provide powerful tools to solve the above problems. Definitions Intuitively, a set of points is a fractal if it exhibits self-similarity over all scales.  ... 
doi:10.1007/978-3-540-39804-2_3 fatcat:vigmo3kq3faivmsu4vebpex7pa

SPECTRUM OF THE LAPLACIAN OF AN ASYMMETRIC FRACTAL GRAPH

Jonathan Jordan
2006 Proceedings of the Edinburgh Mathematical Society  
We consider a simple self-similar sequence of graphs which does not satisfy the symmetry conditions which imply the existence of a spectral decimation property for the eigenvalues of the graph Laplacians  ...  We show that, for this particular sequence, a very similar property to spectral decimation exists, and obtain a complete description of the spectra of the graphs in the sequence.  ...  1 Introduction and definitions 1 .1 Introduction Many self-similar graphs, and related fractals, display a property known as spectral decimation, that the spectrum of the Laplacian can be described  ... 
doi:10.1017/s001309150400063x fatcat:z5frr4ibxfejpmuomfkd7m7b3i

A Study on Gravimeteric Situation in East of Uromieh Lake Region with Determination of Suitable Bouguer Density

Maryam Bayat, Asghar Teymoorian
2015 International Journal of Geography and Geology  
In this paper, the optimal density determined using fractal geometry to Urmia region in this way trying to minimize the topography of the region.  ...  Using this method, we can obtain the Bouguer anomaly optimum density east of Uromieh Lake and turn to the regional gravitation.  ...  a part of curve having fractal property. 10) the tangent line slope is Determined 11) the fractal dimension is obtained the slope.  ... 
doi:10.18488/journal.10/2015.4.9/10.9.146.154 fatcat:vigjpibc75cyzmly4hajgp62tu

Fractal–small-world dichotomy in real-world networks

Gábor Csányi, Balázs Szendrői
2004 Physical Review E  
This distinction is observed in a number of real-world networks, and is related to the degree correlations and geographical constraints.  ...  We conclude by pointing out that the status of human social networks in this dichotomy is far from clear.  ...  The model of [12] embeds a powerlaw graph in a Euclidean lattice, and for some range of parameters, fractal scaling survives.  ... 
doi:10.1103/physreve.70.016122 pmid:15324144 fatcat:5id5q4hf2fgc5b773muyqsbedq

HARMONIC FUNCTIONS AND THE SPECTRUM OF THE LAPLACIAN ON THE SIERPINSKI CARPET

MATTHEW BEGUÉ, TRISTAN KALLONIATIS, ROBERT S. STRICHARTZ
2013 Fractals  
Kusuoka and Zhou have defined the Laplacian on the Sierpinski carpet using average values of functions on small cells and the graph structure of cell adjacency.  ...  As a result we have a wealth of data concerning harmonic functions with prescribed boundary values, and eigenfunctions of the Laplacian with either Neumann or Dirichlet boundary conditions.  ...  work with a graph approximation of the fractal.  ... 
doi:10.1142/s0218348x13500023 fatcat:n76v6rpl3zcgbiwyss2wwf6agu
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