A characterization for sparse -regular pairs.
Domination parameters in random graphs G(n,p), where p is a fixed real number in (0,1), are investigated. We show that with probability tending to 1 as n → ∞, the total and independent domination numbers concentrate on the domination number of G(n,p).
We present a random automorphism-invariant subgraph of a Cayley graph such that with probability 1 its exponential growth rate does not exist.