Independent transversal domination in trees, products and under local changes to a graph

An independent transversal dominating set of a graph G is a set S subset of V(G) that but li dominates G and intersects every maximum independent set of G, and gamma(it) (G) is defined to be the minimum cardinality of an independent transversal dominating set of G. In this paper, we investigate how local changes to a graph effect the independent transversal domination number. We also consider the independent transversal domination number in trees and in the Cartesian and disjunctive product of two graphs. In particular, we show that gamma(it)(Q(n)) = gamma(Q(n)) for n >= 2 where Q(n) is the n-dimensional hypercube and we show gamma(it)(P-m square P-n) = gamma(P-m square P-n) where 5 <= m <= n.