We consider inverse subinterval-nodal problems for the Sturm--Liouville operator on a star graph with mixed boundary conditions in pendant vertices and the standard matching conditions at the interior vertex. Can subinterval nodes recognize star-shaped quantum graphs? In this paper we give a positive answer. It is shown that the data of subinterval-nodes near the interior vertex can uniquely determine the potential on a graph and boundary conditions.
"Reconstruction of the Sturm--Liouville Operator on a Graph from Subinterval Nodes." Taiwanese J. Math. Advance Publication 1 - 12, 2021. https://doi.org/10.11650/tjm/210302