Characteristic functions under series and parallel connection of quantum graphs

TL;DR

This paper derives a formula for the characteristic function of a quantum graph formed by parallel connection of subgraphs, relating it to the characteristic functions of individual subgraphs' boundary problems.

Contribution

It provides a novel expression for the characteristic function of complex quantum graphs based on their subgraph components, enhancing analysis of quantum graph boundary value problems.

Findings

Derived explicit formulas for characteristic functions of parallel-connected quantum graphs.

Established relationships between boundary problems on subgraphs and the entire graph.

Facilitated analysis of quantum graphs with complex connectivity.

Abstract

For a graph consisting of parallel connected subgraphs we express the characteristic function of the boundary value problem with generalized Neumann conditions at both joining points via characteristic functions of different boundary problems on the subgraphs.