In this talk we will give an informal introduction to random walks on graphs and see how typical quantities of interest can be computed with the help of the Markov property.
We will also see how, in the case of the self avoiding random walk, very basic questions remain unanswered and the Markov property, in the usual sense, is lost.
Motivating examples from polymer science and particular graphs and lattices where the self avoiding random walks have been intensively studied will be presented.