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Letbe an  n -vertex complex unit gain graph and let  G  be its underlying graph. The adjacency rank of, written as, is the rank of its adjacency matrix and denote bythe matching number of the underlying graph  G . In this contribution, based on combinatorial interpretation of all the coefficients of the characteristic polynomial of, we determine sharp upper and lower bounds onFurthermore, we establish sharp lower bounds onand. All the corresponding extremal complex unit gain graphs are characterized.

On the relation between the adjacency rank of a complex unit gain graph and the matching number of its underlying graph