Torsional rigidity on metric graphs with delta-vertex conditions
Journal of Mathematical Physics, vol.67, no.6, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 67 Issue: 6
- Publication Date: 2026
- Doi Number: 10.1063/5.0301900
- Journal Name: Journal of Mathematical Physics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Open Archive Collection: AVESIS Open Access Collection
- Dokuz Eylül University Affiliated: Yes
Abstract
We investigate the torsion function (or landscape function) and its associated mass, known as the torsional rigidity, for Laplacians on metric graphs with δ-vertex conditions. We establish a variational characterization of torsional rigidity and derive Hadamard-type formulas, which enable the development of surgical principles. Using these principles, we obtain upper and lower bounds on torsional rigidity and identify extremal graphs within certain classes. We further study the positivity of the torsion function and reduce this question to the positivity of the spectrum of an associated discrete weighted Laplacian. Finally, we explore possible manifestations of Kohler–Jobin-type inequalities in the setting of δ-vertex conditions.