Independence Fractals of Graphs as Models in Architecture

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Adl Maryam; ALIKHANI SAEID; SHOKRI VAHID

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Journal: Mathematics Interdisciplinary Research Year:2019 | Volume:4 | Issue:1 Page(s): 77-86

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Title

Independence Fractals of Graphs as Models in Architecture

Author(s)

Adl Maryam | ALIKHANI SAEID | SHOKRI VAHID | Issue Writer Certificate

Keywords

Independence fractal

structure

model

architecture

Abstract

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) = P ikxk, where ik denote the number of independent sets of cardinality k in G. The Independence fractal of G is the set I(G) = limk! 1 Roots(I(Gk; x) 􀀀 1); where Gk = G[G[ ]], 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 Gk to present some animated structures for building.

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APA: Copy

Adl, Maryam, ALIKHANI, SAEID, & SHOKRI, VAHID. (2019). Independence Fractals of Graphs as Models in Architecture. MATHEMATICS INTERDISCIPLINARY RESEARCH, 4(1), 77-86. SID. https://sid.ir/paper/353665/en

Vancouver: Copy

Adl Maryam, ALIKHANI SAEID, SHOKRI VAHID. Independence Fractals of Graphs as Models in Architecture. MATHEMATICS INTERDISCIPLINARY RESEARCH[Internet]. 2019;4(1):77-86. Available from: https://sid.ir/paper/353665/en

IEEE: Copy

Maryam Adl, SAEID ALIKHANI, and VAHID SHOKRI, “Independence Fractals of Graphs as Models in Architecture,” MATHEMATICS INTERDISCIPLINARY RESEARCH, vol. 4, no. 1, pp. 77–86, 2019, [Online]. Available: https://sid.ir/paper/353665/en

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