This paper examines invariants of the replacement product of two graphs in terms of
the properties of the component graphs. In particular, we present results on the
independence number, the domination number, and the total domination number of
these graphs. The replacement product is a noncommutative graph operation that
has been widely applied in many areas. One of its advantages over other graph
products is its ability to produce sparse graphs. The results in this paper give insight
into how to construct large, sparse graphs with optimal independence or domination
numbers.
Keywords
minimized domination number, total domination number,
maximized independence number, replacement product of a
graph
