We consider a family of graphs generalizing the family of I -graphs, which in turn includes generalized Petersen graphs and prismatic graphs. The paper is devoted to the study of the critical group of a graph that is a cone over a generalized I -graph. The main result of the article is an analog of the Plans theorem (1953), which describes the first homology group of an n -sheeted cyclic cover of the three-dimensional sphere branched over a knot. It asserts that this homology group is almost a direct sum of two copies of a certain abelian group. In this paper, analogous results are established for the structure of the critical group of the graphs under consideration.
I. A. Mednykh (Thu,) studied this question.