Expanded-clique graphs and the domination problem

Abstract

Given a graph G and a function f :In this work, we present two characterizations of the expanded-clique graphs. One of them leads to a linear-time algorithm of recognition. We show that given an expanded-graph H, the domination number of H plus the 2-independence number of the root G of H is equal to |V (G)|. We also show that the domination problem is NP-complete for some subclasses of the expanded-clique graphs.