This has resulted in fellow Exco member Heinz de Boer threatening to take mayor Zandile Gumede to court.
Graham was elected DA eThekwini caucus leader two months ago.
“It’s not going to go well for you in court. I promise you now,” De Boer told the mayor during an executive council meeting.
He also said Gumede did not have a good track record when it came to cases in the high court.
“You cannot prejudice her in this way,” De Boer said.
Earlier, Exco member Mondli Mthembu said the matter of Graham was addressed in a previous full council meeting and a vote was taken. The DA voted for her to be officially made a member of Exco while the ANC decided to abstain from the vote.
Mthembu said the DA then argued if an abstention was a vote or not.
Legal counsel was sought on the matter, Mthembu said.
He said she could only be made a member of Exco after a legal opinion was received, and the matter was tabled at full council.
Mthembu added that the city’s secretariat had made an error in sending Graham an agenda with her name on it.
“In principle, we do not have a problem with Nicole being an Exco member,” he said.
The matter had been previously tabled at Exco and they had also then said it was supposed to be tabled at full council and not Exco, Mthembu said.
Gumede responded to De Boer by saying that fellow Exco member Mondli Mthembu was raising a point on a technical issue.
“It does not bother me. This is an executive committee. If there is a technical error, it needs to be rectified. If there is none, we do have our legal advisers,” she said.
The seat was previously held by Zwakele Mncwango now the KZN provincial leader.
De Boer’s defence of Graham comes in the wake of alleged tension between them.
Last month, the Daily News reported that Graham’s election as caucus leader caused divisions within the party.
DA insiders said Graham had been on a witch-hunt and this was behind De Boer’s resignation as the deputy caucus leader of the party.
Graham had made recommendations to the DA’s federal executive for the removal of De Boer and Sharon Hoosen from Exco.
De Boer’s resignation came barely two weeks after he had been elected deputy caucus leader.