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On deformation of polygonal dendrites preserving the intersection graph. / Drozdov, Dmitry; Samuel, Mary; Tetenov, Andrei.

In: Art of Discrete and Applied Mathematics, Vol. 4, No. 2, P2.07, 17.02.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Drozdov, D, Samuel, M & Tetenov, A 2021, 'On deformation of polygonal dendrites preserving the intersection graph', Art of Discrete and Applied Mathematics, vol. 4, no. 2, P2.07. https://doi.org/10.26493/2590-9770.1375.12a

APA

Drozdov, D., Samuel, M., & Tetenov, A. (2021). On deformation of polygonal dendrites preserving the intersection graph. Art of Discrete and Applied Mathematics, 4(2), [P2.07]. https://doi.org/10.26493/2590-9770.1375.12a

Vancouver

Drozdov D, Samuel M, Tetenov A. On deformation of polygonal dendrites preserving the intersection graph. Art of Discrete and Applied Mathematics. 2021 Feb 17;4(2):P2.07. doi: 10.26493/2590-9770.1375.12a

Author

Drozdov, Dmitry ; Samuel, Mary ; Tetenov, Andrei. / On deformation of polygonal dendrites preserving the intersection graph. In: Art of Discrete and Applied Mathematics. 2021 ; Vol. 4, No. 2.

BibTeX

@article{08250ea625bc402582eddb6c4ad2f5da,
title = "On deformation of polygonal dendrites preserving the intersection graph",
abstract = "Let S = S1, ..., Sm be a system of contracting similarities of R2. The attractor K(S) of the system S is a non-empty compact set satisfying K = S1(K) ∪ ... ∪ Sm(K). We consider contractible polygonal systems S which are defined by a finite family of polygons whose intersection graph is a tree and therefore the attractor K(S) is a dendrite. We find conditions under which a deformation S0 of a contractible polygonal system S has the same intersection graph and therefore the attractor K(S0) is a self-similar dendrite which is isomorphic to the attractor K of the system S.",
keywords = "Attractor, Generalized polygonal system, Index diagram, Intersection graph, Self-similar dendrite",
author = "Dmitry Drozdov and Mary Samuel and Andrei Tetenov",
note = "Funding Information: ∗Supported by Russian Foundation of Basic Research project 18-01-00420 E-mail addresses: dimalek97@yandex.ru (Dmitry Drozdov), marysamuel@iiitl.ac.in (Mary Samuel), atet@mail.ru (Andrei Tetenov) Publisher Copyright: {\textcopyright} 2021 University of Primorska. All Rights Reserved.",
year = "2021",
month = feb,
day = "17",
doi = "10.26493/2590-9770.1375.12a",
language = "English",
volume = "4",
journal = "Art of Discrete and Applied Mathematics",
issn = "2590-9770",
publisher = "University of Primorska",
number = "2",

}

RIS

TY - JOUR

T1 - On deformation of polygonal dendrites preserving the intersection graph

AU - Drozdov, Dmitry

AU - Samuel, Mary

AU - Tetenov, Andrei

N1 - Funding Information: ∗Supported by Russian Foundation of Basic Research project 18-01-00420 E-mail addresses: dimalek97@yandex.ru (Dmitry Drozdov), marysamuel@iiitl.ac.in (Mary Samuel), atet@mail.ru (Andrei Tetenov) Publisher Copyright: © 2021 University of Primorska. All Rights Reserved.

PY - 2021/2/17

Y1 - 2021/2/17

N2 - Let S = S1, ..., Sm be a system of contracting similarities of R2. The attractor K(S) of the system S is a non-empty compact set satisfying K = S1(K) ∪ ... ∪ Sm(K). We consider contractible polygonal systems S which are defined by a finite family of polygons whose intersection graph is a tree and therefore the attractor K(S) is a dendrite. We find conditions under which a deformation S0 of a contractible polygonal system S has the same intersection graph and therefore the attractor K(S0) is a self-similar dendrite which is isomorphic to the attractor K of the system S.

AB - Let S = S1, ..., Sm be a system of contracting similarities of R2. The attractor K(S) of the system S is a non-empty compact set satisfying K = S1(K) ∪ ... ∪ Sm(K). We consider contractible polygonal systems S which are defined by a finite family of polygons whose intersection graph is a tree and therefore the attractor K(S) is a dendrite. We find conditions under which a deformation S0 of a contractible polygonal system S has the same intersection graph and therefore the attractor K(S0) is a self-similar dendrite which is isomorphic to the attractor K of the system S.

KW - Attractor

KW - Generalized polygonal system

KW - Index diagram

KW - Intersection graph

KW - Self-similar dendrite

UR - http://www.scopus.com/inward/record.url?scp=85112553053&partnerID=8YFLogxK

U2 - 10.26493/2590-9770.1375.12a

DO - 10.26493/2590-9770.1375.12a

M3 - Article

AN - SCOPUS:85112553053

VL - 4

JO - Art of Discrete and Applied Mathematics

JF - Art of Discrete and Applied Mathematics

SN - 2590-9770

IS - 2

M1 - P2.07

ER -

ID: 34439015