@article{Boyko_Martynyuk_Pivovarchik_2024, title={On the scattering problem and problem of recovery of the shape of a graph}, volume={76}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/8151}, DOI={10.3842/umzh.v76i8.8151}, abstractNote={<p>UDC 517.9</p> <p>We consider a scattering problem generated by the Sturmâ€“Liouville equation on a tree formed by an equilateral compact subtree with a lead (a half-infinite edge) attached to this compact subtree. <span class="Apple-converted-space"> </span>It is assumed that the potential on the lead by is identically equal to zero and the potentials on finite edges are real $L_2$-functions. <span class="Apple-converted-space"> </span>We show how to determine the shape of the tree by using the S-function and the eigenvalues of the scattering problem.<span class="Apple-converted-space"> </span></p>}, number={8}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={BoykoO. and MartynyukO. and PivovarchikV.}, year={2024}, month={Sep.}, pages={1120 - 1131} }