Our teacher told us that a carbocation connected to 3 cyclopropane rings is among the most stable carbocations. But I am unable to understand how, as resonance (the most important factor governing stability) is absent. How did other factors bring so much stability?
Your teacher is correct, that
a carbocation connected to 3 cyclopropane rings is among the most stable carbocations.
This because of various electrical effects, such as:
The Inductive Effect
The Mesomeric Effect
Here's a link for you, to study them: Click Here. Please make sure that you learn this correctly and from standard resources, in order to avoid confusion.
There may be a little confusion between mesomeric effect and resonance effect, so here's another link just to avoid confusion. : refer to the answer by Maria Dar
Please, do ask your teacher to help you understand this topic better :-)