Pat Rice, who played in the Arsenal Double-winning side of 1970-71 and is currently youth team coach with the club, was immediately installed as the favourite. He can point to years steeped in the traditions of the marbled halls and a team that presently lead the South-East Counties League, but many will question whether someone with no experience of League management can guide the club back to the top.
Much the same applies to Stewart Houston, Graham's No 2, who was in charge of the team for last night's game against Nottingham Forest, and may be asked to continue in the role until the end of the seaon. Houston came to Highbury in 1987 as reserve team coach and took over as Graham's second- in-command three years later.
Arsenal's tradition of appointing managers with experience of the club means that two former Highbury idols, Liam Brady and David O'Leary, have been widely touted for a return, possibly even in tandem. Again there would be doubters. O'Leary is currently with Leeds, and has never managed, while Brady's experience has hardly been of the eye-catching variety.
He left Celtic in October 1993 having failed to undermine Rangers dominace significantly, and despite having made some progress with Brighton, their present position - 17th in the Second Division - scarcely demands a move to the Premiership. The career of another old boy, Alan Ball, appeared to be in decline until its recent renaissance with Southampton.
Peter Hill-Wood, the Arsenal chairman said yesterday that the club wouldn't "rule out other contenders". David Pleat of Luton has been frequently linked with a move to N5, but though his Tottenham background is unlikely to count against him, the circumstances surrounding his departure from White Hart Lane might.
Highbury heritage aside, Bolton's Bruce Rioch and Colin Todd surely merit consideration as do Wycombe's Martin O'Neill and Steve Coppell - despite his presence on the Premiership inquiry - especially since he made it clear last week that he was keen to return to management.