All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is worthy to mention that swearing by divorce is impermissible. The Prophet, sallallaahu ‘alayhi wa sallam, said:
"Whoever has to take an oath should swear by Allaah or otherwise remain silent." [Al-Bukhari and Muslim]
As for that man who swore by divorce not to talk to his cousin again, the majority of scholars believe that this type of oath is considered a conditional divorce; whenever he breaks his oath, the divorce becomes effective.
However, some scholars, including Shaykh-ul-Islam Ibn Taymiyyah believed that the oath of divorce only requires expiation of the oath.