Abstract: A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components. The k-connected domination number γ_c^k(G) of G is the minimum cardinality taken over all minimal k-connected dominating sets of G. In this paper, we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.

Key words: connected domination number, 2-connected domination number, trees, unicyclic graphs