The Plans Theorem for Cones over Generalized $ I $-Graphs
Abstract
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.
Fields of Study & Subjects
Graph theory and applications
Advanced Graph Theory Research
Finite Group Theory Research
Publication details
- Journal / source
- Siberian Mathematical Journal
- Volume
- 67
- Issue
- 1
- Pages
- 99–109
- Publication date
- 1 January 2026
- Language
- EN