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In this paper, we focus on the diversity order of the decode-and-forward (DF) cooperative networks with relay selection. Many detection schemes have been proposed for the DF; but it has been shown that the cooperative maximum ratio combining (C-MRC) can achieve almost the same performance as the optimum maximum likelihood detector and has a much lower complexity. Therefore, we first combine the C-MRC with the relay selection and show that it achieves the full diversity order by deriving an upper bound of its average bit error rate (BER). In order to reduce the signaling overhead, we then combine the link-adaptive regeneration (LAR) with the relay selection. By deriving an upper bound of the average BER, we show that, when there are two relays, the diversity order of the LAR with relay selection is upper-bounded by three and lower-bounded by 3 - epsiv, where xi is an arbitrarily small positive number.