Resistance diameters and critical probabilities of Cayley graphs on irreducible complex reflection groups

Abstract

We consider networks on minimal Cayley graphs of irreducible complex reflection groups G(m, p, n). We show that resistance diameters of these graphs have asymptotic \(\Theta (1/n)\) as \(n\rightarrow \infty \) under fixed m, p. Non-trivial lower and upper asymptotic bounds for critical probabilities of percolation for there appearing a giant connected component have been obtained.