ON THE EIGENVALUES OF THE DISCRETE LAPLACE OPERATOR ON COMBINATORIAL GRAPHS
Keywords:
Graphs, connected components, Laplace operator, spectrum, eigenvalue.Abstract
We study discrete and metric graphs and some of their properties. We define a Laplace operator acting on a graph as a difference operator and investigate its spectral properties. Moreover, we learn its eigenvalues and eigenvectors that represent the stationary states (wavefunctions) of the considered system. A relation between the number of connected components of a graph and multiplicity of 0 as an eigenvalue of the corresponding Laplace operator is established in examples.
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