\input zb-basic \input zb-ioport \iteman{io-port 05584881} \itemau{Wang, Shiying; Guo, Jiwen} \itemti{Primitive exponents of a class of $(k+1)$-colored directed graphs.} \itemso{Math. Appl. 21, No. 4, 778-786 (2008).} \itemab Summary: In this paper, we define $(k+1)$-colored directed graphs $D \cal{A}$ with $(k+1)$-cycles and give a necessary and sufficient condition for these directed graphs to be primitive. We obtain the primitive exponent of directed graphs $D \cal{A}$ at the same time. \itemrv{~} \itemcc{} \itemut{cycle; colored digraph; primitive exponent} \itemli{} \end