Consider a cyclic directed graph $G$, is it true that the power series computation of its adjacency matrix $M$ can stop after $k$ steps, being $k$ the directed diameter of $G$, "converging" to a point in which every node in the graph has been reached with any other?

I try to prove this considering the linear independence of the first $k$ powers of $M$. Am I wrong or this holds for directed cyclic graphs too?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.