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On the critical group of graph \(P_n\times C_4\). (Chinese. English summary) Zbl 1150.05360

Summary: The critical group of a graph is a refinement of the number of spanning trees of the graph. It is a subtle isomorphism invariant of the graph. In this paper, the structure of the critical group of the Cartesian products graph \(P_n\times C_4\) is direct sum of two or three cyclic groups.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)