Extended Graph of Fuzzy Topographic Topological Mapping Model: G04(FTTMn4)

Abstract

Fuzzy topological topographic mapping (FTTM) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. The key to the model is its topological structure that can accommodate electrical or magnetic recorded brain signal. A sequence of FTTM, FTTMn, is an extension of FTTM whereby its form can be arranged in a symmetrical form, i.e., polygon. The special characteristic of FTTM, namely, the homeomorphisms between its components, allows the generation of new FTTM. The generated FTTMs can be represented as pseudo graphs. A pseudo-graph consists of vertices that signify the generated FTTM and edges that connect their incidence components. A graph of pseudo degree zero, G0(FTTMnk ), however, is a special type of graph where each of the FTTM components differs from its adjacent. A researcher posted a conjecture on G03(FTTMn3) in 2014, and it was finally proven in 2021 by researchers who used their novel grid-based method. In this paper, the extended G03(FTTMn3), namely, the conjecture on G04(FTTMn4) that was posed in 2018, is narrated and proven using simple mathematical induction.