I'm not sure dog panting is primarily a method for communicating amongst each other, but more of a method of communicating with humans if there's something wrong with the dog. And even then, the panting isn't actually intended as a form of communication, but more so a reaction to something that may have gone awry.
When it's hot outside, dogs pant to cool off. They have no sweat glands, so that big tongue hanging out of their mouths and all that additional cool air circulating through their lungs assists with body cooling. Dogs also pant for a variety of health reasons. If a dogs begins panting heavily out of nowhere and for no apparent reason, it's time to call a veterinarian. There may be something amiss with the animal.
People often ask themselves: Why is my dog panting when he or she is just lying there doing nothing?
There are four primary reasons for this.
1. It's heat related. The dog is trying to cool off.
2. The dog is in pain. The panting is a response to that.
3. The dog has anxiety regarding something in his or her surroundings. Many dogs pant heavily during thunderstorms.
4. The dog has a disease that needs to be addressed.
Any more questions? Please ask!