To characterize the singularity of all mixed trees and some mixed circles,the ranks of mixed graphs and digraphs are described by some results of unoriented graphs or digraphs and knowledge of linear algebra.The results are as follows:a mixed tree is nonsingular if and only if it has a perfect match and every edge in the perfect match is undirected;the n-order mixed cycle with only one unoriented edge is nonsingular if and only if n-1 arcs are directed;the mixed cycle with an arc is nonsingular if and only if n≠0(mod4);an arc-edge staggered n-order mixed cycle is nonsingular if and only if n=2(mod 4).
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