The structure of sandpile groups of outerplanar graphs

• We did a general review of the manuscript checking grammar and typos suggested by reviewers. have added three SAGE codes Reviewer #1. #1 to include statistics comparing with other computer algebra system. However, we consider that this goes beyond aim our since objective is not focus on performance algorithms, rather are introducing methodology compute algebraic combinatorial structure outerplanar graphs. sandpile groups families planar graphs having common weak dual evaluating indeterminates critical ideals at lengths cycles bounding interior faces. This method allows us determine graphs, can be used many graph families. Finally, identity element for outerplane