Rules, boundaries, requirements, hunt or no hunt, access, permit or no permit, etc. seem to change from year to year for many lakes. Especially small city lakes. For example there was an earlier discussion on a city lake that just closed access recently. The only way your going to get the most correct up to date answer is to contact the lakes controlling authority. Especially since you live there. Taking someones anonymous word from an online forum, could get you in trouble. Contact info for Graham and other lakes around you are on this page. Good Luck.
http://www.tpwd.texas.gov/fishboat/fish/recreational/lakes/inpanhd.phtml