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The independence fractal of a graph

2003
*
Journal of combinatorial theory. Series B (Print)
*

We prove that in fact they converge (in

doi:10.1016/s0095-8956(02)00014-x
fatcat:7esq4zbqvzaizeged4sdfufj6a
*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 ...##
###
Independence roots and independence fractals of certain graphs

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*. ...

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

2018
*
Journal of Production Engineering
*

Intelligent systems are

doi:10.24867/jpe-2018-01-021
fatcat:ee5jl2vtnvejpdz7l6wqgah3tm
*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. ...##
###
Some Combinatorial Problems in Power-Law Graphs

2021
*
Computer journal
*

For both

doi:10.1093/comjnl/bxab007
fatcat:xtcxwvqzlrc5boq2d2on2glebm
*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. ...##
###
The duality of fractals: roughness and self-similarity

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. ...

##
###
The k-fractal of a simplicial complex

2004
*
Discrete Mathematics
*

We prove that they converge to

doi:10.1016/j.disc.2003.12.014
fatcat:5mxaytz5r5gx7njcb47zif537a
*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. ...##
###
AN ANALYSIS OF STABILITY OF TRENDS IN MUTUAL FUNDS USING FRACTAL DIMENSION INDEX (FDI) COMPUTED FROM HURST EXPONENTS

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. ...

##
###
Phase ordering and universality for continuous symmetry models on graphs

2009
*
Journal of Statistical Mechanics: Theory and Experiment
*

We study

doi:10.1088/1742-5468/2009/02/p02040
fatcat:pihlvgndijarhio4jgzxexivnq
*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*. ...##
###
DESIGN AND SIMULATION OF SIERPINSKI CARPET FRACTAL ANTENNA AND COMPARISION OF DIFFERENT FEEDS

2014
*
International Journal of Research in Engineering and Technology
*

In this paper,

doi:10.15623/ijret.2014.0316007
fatcat:pmbh24dzi5a2jdywzp4x6cqc6u
*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. ...##
###
Next Generation Data Mining Tools: Power Laws and Self-similarity for Graphs, Streams and Traditional Data
[chapter]

2003
*
Lecture Notes in Computer Science
*

How about

doi:10.1007/978-3-540-39857-8_3
fatcat:oxs62jcyp5huzjzbikx2szn2ki
*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. ...##
###
Next Generation Data Mining Tools: Power Laws and Self-similarity for Graphs, Streams and Traditional Data
[chapter]

2003
*
Lecture Notes in Computer Science
*

How about

doi:10.1007/978-3-540-39804-2_3
fatcat:vigmo3kq3faivmsu4vebpex7pa
*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. ...##
###
SPECTRUM OF THE LAPLACIAN OF AN ASYMMETRIC FRACTAL GRAPH

2006
*
Proceedings of the Edinburgh Mathematical Society
*

We consider

doi:10.1017/s001309150400063x
fatcat:z5frr4ibxfejpmuomfkd7m7b3i
*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 ...##
###
A Study on Gravimeteric Situation in East of Uromieh Lake Region with Determination of Suitable Bouguer Density

2015
*
International Journal of Geography and Geology
*

In this paper,

doi:10.18488/journal.10/2015.4.9/10.9.146.154
fatcat:vigjpibc75cyzmly4hajgp62tu
*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. ...##
###
Fractal–small-world dichotomy in real-world networks

2004
*
Physical Review E
*

This distinction is observed in

doi:10.1103/physreve.70.016122
pmid:15324144
fatcat:5id5q4hf2fgc5b773muyqsbedq
*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. ...##
###
HARMONIC FUNCTIONS AND THE SPECTRUM OF THE LAPLACIAN ON THE SIERPINSKI CARPET

2013
*
Fractals
*

Kusuoka and Zhou have defined

doi:10.1142/s0218348x13500023
fatcat:n76v6rpl3zcgbiwyss2wwf6agu
*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*. ...
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