Connected Degree Equitable Domination in Graphs

Let G be a connected graph. A subset S ⊆ V (G) is an equitable dominating set in G if for each vertex not in S there exists u ∈ S such that uv ∈ E(G) and | degG u − degG v| ≤ 1 . An equitable dominating set S ⊆ V (G) is called a connected equitable dominating set of G if the subgraph ⟨S⟩ induced by S is connected . The minimum cardinality of such connected equitabledominating sets in G is called the connected equitable domination number of G and is denoted by γce(G). This paper investigates the connected equitable domination in the join and corona of graphs. The connected equitable dominating sets in the join and corona of graphs are characterized and, as direct consequences, the connected equitable domination numbers of these graphs are obtained. In addition, a n exact value of some families of graphs and a realization problem are established.