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.
Disclosure statement
No potential conflict of interest was reported by the authors.