Expanded-clique graphs and the domination problem
Abstract
Given a graph G such that each vertex vi has a value f(vi), the expanded-clique graph H is the graph where each vertex vi of G becomes a clique Vi of size f(vi) and for each edge vivj ∈ E(G), there is a vertex of Vi adjacent to an exclusive vertex of Vj. In this work, among the results, we present two characterizations of the expanded-clique graphs, one of them leads to a linear-time recognition algorithm. Regarding the domination number, we show that this problem is -complete for planar bipartite 3-expanded-clique graphs and for cubic line graphs of bipartite graphs.
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