Hossain, Sk Asfaq2023-12-142023-12-142023-12162p.http://hdl.handle.net/10263/7422This thesis is under the supervision of Prof. Debashish GoswamiWe introduce various notions of quantum symmetry in a directed or undi- rected multigraph with no isolated vertex and explore relations among them. If the multigraph is simple (with or without loops), all our notions of quantum symmetry reduce to the already existing notions of quantum symmetry provided by Bichon and Banica. Using the machinery developed, we have also provided applications of quantum symmetry in some mathematical and physical models.enQuantum SymmetryMultigraphsPotts ModelNon-commutative GeometryThesis