Annotation: Isogeny graphs of supersingular elliptic curves are one of perspective mathematical structures for post-quantum cryptography algorithms. However, recently published attack on the SIDH protocol [1] demonstrates that isogeny graphs require a more detailed study when they are used in real protocols. In this paper, we analyze the structure of isogeny graphs of degree D > 3 and consider a set of nodes of a special kind to which the attack [7] on path recovery in the graph is applicable.

Keywords: post-quantum cryptography, isogeny graphs.