The former St Helens captain, now with Canterbury Bulldogs, could be banned for up to three months if he is found guilty of one of the most "heinous crimes" in rugby league.
Graham was put on report after Melbourne full-back Slater made the allegation during his side's 14-4 win over the Bulldogs and, as expected, the case was referred directly to the judiciary after the match review committee met on Monday morning.
The case would normally be heard on Wednesday but the Bulldogs have asked for it to be put back to later in the week to avoid a clash with their club presentation.
The general consensus is Graham is staring at a suspension of between eight and 12 weeks.
Canterbury's Brad Morrin was banned for eight games in 2007 for biting Timana Tahu, while Titans utility back William Zillman copped a month for the same offence in 2009.
Both those players were biting into arms whereas Graham's is considered more serious due to the fact he is alleged to have attacked Slater's ear.
Graham is due to link up with England next week for their high-altitude training camp in South Africa and, if suspended, will miss their autumn international matches against France and Wales.
The skilful prop, who captained England in the 2010 Four Nations Series, had created a big impression on his first season in the NRL but his reputation is now in danger of being tarnished.