Domination-related parameters in middle graphs.

The middle graph M (G) of a graph G is the graph obtained by subdividing each edge of G exactly once and joining all these newly introduced vertices of adjacent edges of G. It is known that the decision problems for Italian domination number γ I (G) , 2 -rainbow domination number γ r 2 (G) and Roman domination number γ R (G) are NP-complete. Recently, it was proved that γ I (M (G)) = γ r 2 (M (G)) = γ R (M (G)) = n for a graph G of order n. In this paper, we continue to study several domination and domatic numbers in middle graphs. We also obtain closed formulas for domination, secure domination and total domination numbers in middle graphs of rooted product graphs. [ABSTRACT FROM AUTHOR]