Extended Graph of the Fuzzy Topographic Topological Mapping Model

Fuzzy topological topographic mapping (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics>...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Muhammad Zillullah Mukaram, Tahir Ahmad, Norma Alias, Noorsufia Abd Shukor, Faridah Mustapha
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	<i>FTTM</i> graph pseudo degree sequence Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/377aca7a54df40908229f39545c39ef8
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:377aca7a54df40908229f39545c39ef8
record_format	dspace
spelling	oai:doaj.org-article:377aca7a54df40908229f39545c39ef82021-11-25T19:07:33ZExtended Graph of the Fuzzy Topographic Topological Mapping Model10.3390/sym131122032073-8994https://doaj.org/article/377aca7a54df40908229f39545c39ef82021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2203https://doaj.org/toc/2073-8994Fuzzy topological topographic mapping (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula>) is a mathematical model which consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of <i>FTTM</i>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><msub><mi>M</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula>, is an extension of <i>FTTM</i> that is arranged in a symmetrical form. The special characteristic of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula>, namely the homeomorphisms between its components, allows the generation of new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula>. The generated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula>s can be represented as pseudo graphs. A graph of pseudo degree zero is a special type of graph where each of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula> components differs from the one adjacent to it. Previous researchers have investigated and conjectured the number of generated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula> pseudo degree zero with respect to <i>n</i> number of components and <i>k</i> number of versions. In this paper, the conjecture is proven analytically for the first time using a newly developed grid-based method. Some definitions and properties of the novel grid-based method are introduced and developed along the way. The developed definitions and properties of the method are then assembled to prove the conjecture. The grid-based technique is simple yet offers some visualization features of the conjecture.Muhammad Zillullah MukaramTahir AhmadNorma AliasNoorsufia Abd ShukorFaridah MustaphaMDPI AGarticle<i>FTTM</i>graphpseudo degreesequenceMathematicsQA1-939ENSymmetry, Vol 13, Iss 2203, p 2203 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	<i>FTTM</i> graph pseudo degree sequence Mathematics QA1-939
spellingShingle	<i>FTTM</i> graph pseudo degree sequence Mathematics QA1-939 Muhammad Zillullah Mukaram Tahir Ahmad Norma Alias Noorsufia Abd Shukor Faridah Mustapha Extended Graph of the Fuzzy Topographic Topological Mapping Model
description	Fuzzy topological topographic mapping (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula>) is a mathematical model which consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of <i>FTTM</i>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><msub><mi>M</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula>, is an extension of <i>FTTM</i> that is arranged in a symmetrical form. The special characteristic of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula>, namely the homeomorphisms between its components, allows the generation of new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula>. The generated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula>s can be represented as pseudo graphs. A graph of pseudo degree zero is a special type of graph where each of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula> components differs from the one adjacent to it. Previous researchers have investigated and conjectured the number of generated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>T</mi><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula> pseudo degree zero with respect to <i>n</i> number of components and <i>k</i> number of versions. In this paper, the conjecture is proven analytically for the first time using a newly developed grid-based method. Some definitions and properties of the novel grid-based method are introduced and developed along the way. The developed definitions and properties of the method are then assembled to prove the conjecture. The grid-based technique is simple yet offers some visualization features of the conjecture.
format	article
author	Muhammad Zillullah Mukaram Tahir Ahmad Norma Alias Noorsufia Abd Shukor Faridah Mustapha
author_facet	Muhammad Zillullah Mukaram Tahir Ahmad Norma Alias Noorsufia Abd Shukor Faridah Mustapha
author_sort	Muhammad Zillullah Mukaram
title	Extended Graph of the Fuzzy Topographic Topological Mapping Model
title_short	Extended Graph of the Fuzzy Topographic Topological Mapping Model
title_full	Extended Graph of the Fuzzy Topographic Topological Mapping Model
title_fullStr	Extended Graph of the Fuzzy Topographic Topological Mapping Model
title_full_unstemmed	Extended Graph of the Fuzzy Topographic Topological Mapping Model
title_sort	extended graph of the fuzzy topographic topological mapping model
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/377aca7a54df40908229f39545c39ef8
work_keys_str_mv	AT muhammadzillullahmukaram extendedgraphofthefuzzytopographictopologicalmappingmodel AT tahirahmad extendedgraphofthefuzzytopographictopologicalmappingmodel AT normaalias extendedgraphofthefuzzytopographictopologicalmappingmodel AT noorsufiaabdshukor extendedgraphofthefuzzytopographictopologicalmappingmodel AT faridahmustapha extendedgraphofthefuzzytopographictopologicalmappingmodel
_version_	1718410270415519744

Extended Graph of the Fuzzy Topographic Topological Mapping Model

Ejemplares similares