ACTA

Some Applications of Generalized Euler Characteristic of Quantum Graphs and Microwave Networks

S. Bauch^a, M. Lawniczak^a, J. Wrochna^a, P. Kurasov^b, L. Sirko^a
^aInstitute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
^bDepartment of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden

Full Text PDF

In this article we continue to explore the possibilities offered by our discovery that one of the main graph and network characteristic, the generalized Euler characteristic i_G, can be determined from a graph/network spectrum. We show that using the generalized Euler characteristic i_G the number of vertices with Dirichlet |V_D| boundary conditions of a family of graphs/networks created on the basis of the standard quantum graphs or microwave networks can be easily identified. We also present a new application of the generalized Euler characteristic for checking the completeness of graphs/networks spectra in the low energy range.

DOI:10.12693/APhysPolA.140.525
topics: quantum graphs, Euler characteristic, boundary conditions, microwave networks