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We construct several new families of directed strongly regular Cayley graphs (DSRCGs) over the metacyclic group M 4 n = 〈 a , b | a n = b 4 = 1 , b − 1 a b = a − 1 〉 , some of which generalize those earlier constructions. For a prime p and a positive integer α > 1 , for some cases, we characterize the DSRCGs over M 4 p α .

Directed Strongly Regular Cayley Graphs over Metacyclic Groups of Order 4n