Quantum graphs: an introduction and a brief survey

TL;DR

This paper introduces the fundamental concepts of quantum graphs, surveys key research areas, and provides references to further literature, serving as an accessible overview for newcomers and researchers.

Contribution

It offers a concise introduction and survey of quantum graphs, highlighting main topics and guiding readers to relevant literature.

Findings

Identifies core notions of quantum graphs

Highlights active research areas in quantum graph theory

Provides references to foundational and recent literature

Abstract

The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary, i.e. they refer to other surveys.