TY - JOUR
ID - 93388
TI - Independence Fractals of Graphs as Models in Architecture
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Adl, Maryam
AU - Alikhani, Saeid
AU - Shokri, Vahid
AD - Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
AD - Department of Mathematics, Yazd University, Yazd, Iran
Y1 - 2019
PY - 2019
VL - 4
IS - 1
SP - 77
EP - 86
KW - Independence fractal
KW - structure
KW - model
KW - Architecture
DO - 10.22052/mir.2019.169780.1112
N2 - 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.
UR - http://mir.kashanu.ac.ir/article_93388.html
L1 - http://mir.kashanu.ac.ir/article_93388_7892f236158e0d094cd6873f94de7f46.pdf
ER -