%0 Journal Article
%T Independence Fractals of Graphs as Models in Architecture
%J Mathematics Interdisciplinary Research
%I University of Kashan
%Z 2538-3639
%A Adl, Maryam
%A Alikhani, Saeid
%A Shokri, Vahid
%D 2019
%\ 06/01/2019
%V 4
%N 1
%P 77-86
%! Independence Fractals of Graphs as Models in Architecture
%K Independence fractal
%K structure
%K model
%K Architecture
%R 10.22052/mir.2019.169780.1112
%X Architectural science requires interdisciplinary science interconnection in order to improve this science. Graph theory and geometrical fractal are two examples of branches of mathematics which have applications in architecture and design. In architecture, the vertices are the rooms and the edges are the direct connections between each two rooms. The independence polynomial of a graph $G$ is the polynomial $I(G,x)=sum i_kx^k$, where $i_k$ denote the number of independent sets of cardinality $k$ in $G$. The independence fractal of $G$ is the set ${cal I}(G)=lim _{krightarrow infty} Roots (I({G^{k}},x)-1), $ where $G^{k}=G[G[cdots]]$, and $G[H]$ is the lexicographic product for two graphs $G$ and $H$. In this paper, we consider graphical presentation of a ground plane as a graph $G$ and use the sequences of limit roots of independence polynomials of $G^k$ to present some animated structures for building.
%U http://mir.kashanu.ac.ir/article_93388_7892f236158e0d094cd6873f94de7f46.pdf