Detecting non-isomorphic strongly regular graphs via entanglement entropy in spinless free fermion model

In this research, the graph isomorphism problem is investigated in the non-isomorphic strongly regular graphs, which are a class of regular graphs with high symmetry. Classical and quantum algorithms often fail to detect all non-isomorphic strongly regular graphs. Our approach is applying the entanglement entropy, which is calculated for all kinds of partitions in graphs. The spinless free fermion Hamiltonian is considered in this research where its hopping matrix is given by the adjacency matrix of the graph. We show that all chosen sets of non-isomorphic strongly regular graphs distinguish from each other by using fermionic entanglement entropy.