Mukaram, Muhammad Zillullah and Ahmad, Tahir and Alias, Norma and Abd. Shukor, Noorsufia and Mustapha, Faridah (2021) Extended graph of the fuzzy topographic topological mapping model. Symmetry, 13 (11). pp. 115. ISSN 20738994

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Official URL: http://dx.doi.org/10.3390/sym13112203
Abstract
Fuzzy topological topographic mapping (TTTM) is a mathematical model which consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM, TTTMn, is an extension of FTTM that is arranged in a symmetrical form. The special characteristic of TTTM, namely the homeomorphisms between its components, allows the generation of new TTTM. The generated FTTMs can be represented as pseudo graphs. A graph of pseudo degree zero is a special type of graph where each of the FTTM components differs from the one adjacent to it. Previous researchers have investigated and conjectured the number of generated FTTM pseudo degree zero with respect to n number of components and k number of versions. In this paper, the conjecture is proven analytically for the first time using a newly developed gridbased 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.
Item Type:  Article 

Uncontrolled Keywords:  graph, pseudo degree, sequence 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  94812 
Deposited By:  Yanti Mohd Shah 
Deposited On:  29 Apr 2022 22:27 
Last Modified:  29 Apr 2022 22:27 
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