Just curious because children keep drawing chalk in my neighbor’s and I driveway. I am also curious if we have the right to regulate street laws on the street we live on?
With respect of Graffiti, this generally fall under vandalism, and with respect of Ohio law, chalk is unlikely to qualify under Ohio Revised Code Title XXIX. Crimes Procedure as there is unlikely to be any lasting damage.
Depending on what is being written, you might be able to do something about it under disorderly conduct laws.
If your concern is just that they're marking up your driveway without your permission, it probably doesn't matter whether it's "graffiti" as much as it matters whether it's illegal.
I can't find a record of any prosecution for the use of sidewalk chalk, but the behavior sounds like it fits within the description of criminal mischief (R.C. 2909.07):
No person shall ... Without privilege to do so, knowingly ... deface ... The property of another....
Except as otherwise provided in this division, criminal mischief ... is a misdemeanor of the third degree.
And coming into your driveway (I'm assuming you aren't complaining about chalk that is just on the sidewalk) would probably be criminal trespass if you have notified them that they may not be there.
This all assumes that you (or you and your neighbor) are the only ones with the rights to this driveway. If we're dealing with a driveway into a building with six units and children from other units are drawing on it, you're probably not going to get anywhere trying to stop them.