Graham said his decision was not based on any specific issue the commission was facing.
"It's just not the right thing to do at this time," he said.
Paulding School Board member Richard Manous filed to qualify for Graham's seat in the May 20 Republican primary. He joins former Paulding Republican Party chairman Vernon Collett, who filed Monday for the Post 3 seat.
In addition, a Democrat has filed paperwork to qualify to seek her party's nomination for the commission's Post 2 seat.
Patti Smith, a longtime Paulding resident, will seek her party's nomination in the May 20 primary. If she wins, she would face incumbent Commissioner Todd Pownall in the November general election. Pownall, who has served one term, is the only Republican who has filed for the post.
Smith, who lives near Silver Comet Field, and Pownall have been vocal critics of a plan for commercial airline service at the airport off Rockmart Highway.
In Georgia General Assembly races, former longtime Georgia House member Bill Hembree of Winston has qualifed to challenge incumbent State Sen. Mike Dugan, R-Carrollton, for the Republican nomination for the Senate District 30 seat.
Hembree, a Douglasville insurance agent, served nine full terms representing House District 67 from 1992 to 1996 and from 1999 to 2012.
He resigned his House seat in 2012 to run in a special election for the District 30 Senate seat after Bill Hambrick was appointed to a judgeship. Hembree was the top vote-getter in the Republican primary in that election, but Dugan forced Hembree into a runoff where Dugan defeated Hembree. Dugan then defeated Libertarian candidate James Camp to win the Senate seat.
In addition, Kim Alexander, a Paulding native, qualified to seek the Democratic nomination, and former state House member Bob Snelling qualified to seek the Republican nomination, for the House District 66 seat. In 2012, Alexander defeated Snelling for the seat which represents a district that includes Paulding and Douglas counties.
Candidates who have turned in paperwork to qualify for Paulding County local and state offices include:
Todd Pownall (I)
David Barnett (I)
Nick Chester (I)
Sammy McClure (I)
Kim Curl (I)
Dick Donovan (I)
Superior Court Judge:
James Osborne (I)
State House of Representatives:
Howard Maxwell (I)
Paulette Braddock (I)
Kim Alexander (I)
Micah Gravley (I)
Mike Dugan (I)
Bill Heath (I)
I - incumbent