The sandpile groups of chain-cyclic graphs

Firstly, we consider the graphs obtained by gluing a family of arbitrary finite graphs to the edges of a cyclic graph and prove that the sandpile group of the resulting graph does not depend on a specific way of doing that. Then, we define the class of chain-cyclic graphs, which are the graphs obtained by connecting a finite family of cyclic graphs along a line. Two kinds of formulas for calculating the sandpile groups of chain-cyclic graphs are proved.