On the spectra of Laplace operator on the Icosahedron metric graph
Hendri Maulana, Yudi Soeharyadi, Oki Neswan.

Faculty of Mathematics and Natural Science, Bandung Institute of Technology, Bandung, Indonesia

Abstract

This study focuses on the eigenvalue problem of the Laplace operator on the Icosahedron metric graph. It is part of a more general problem into the eigenvalues of the Laplace operator on metric graphs of Platonic solids. A compact metric graph is defined as a graph where edges are represented by finite line segments, enabling the application of one-dimensional calculus to be done on this structure. In this study, the Neumann-Kirchhoff conditions, along with compatibility conditions are applied to the metric graph. We carried on the explicit computations of the eigenvalues using symbolic computer algebra Wolfram Mathematica. Our results match with those obtained by Lipovsky and Exner (2019), via advanced operator decomposition theoretic tools.

Keywords: Eigen values of Laplace operator, Icosahedron metric graph, continuity condition, kirchhoff condition.

Topic: Minisymposia Differential Equations