Geodesic
Sandpile groups and the join of graphs
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXII, Tome 411 (2013), pp. 119-124

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We introduce the procedure of joining two graphs by identifying an arbitrary pair of their vertices. The main result is that the sandpile group of the join of several finite graphs is the direct product of the sandpile groups of the components. Some consequences are derived. 
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     author = {I. A. Krepkiy},
     title = {Sandpile groups and the join of graphs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {119--124},
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     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_411_a6/}
}
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I. A. Krepkiy. Sandpile groups and the join of graphs. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXII, Tome 411 (2013), pp. 119-124. http://geodesic.mathdoc.fr/item/ZNSL_2013_411_a6/