Abstract
Let be a cycle of length k + 1 and be a cycle of length t + 1. A polygon flower with two centers, denoted by is obtained by identifying the edge of with an edge ei that belongs to an end-polygon of Pi for and identifying the edge of with an edge ej that belongs to an end-polygon of Pj for where and have a common edge h. In this paper, we determine the order of sandpile group S(F) of F, which can be viewed as generalized of results in paper (Haiyan Chen, Bojan Mohar. The sandpile group of a polygon flower. Discrete Applied Mathematics, 2019). Moreover, the formula and structure for sandpile group of polygon flower can be obtained. Finally, as application of our result, we also present the sandpile group of cata-condensed system with two branched hexagons.
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