On graphs with equal total domination and connected domination numbers

A subset SS of VV is called a total dominating set   if every vertex in VV is adjacent to some vertex in SS. The total domination number  γt(G)γt(G) of GG is the minimum cardinality taken over all total dominating sets of GG. A dominating set is called a connected dominating set   if the induced subgraph 〈S〉〈S〉 is connected. The connected domination number  γc(G)γc(G) of GG is the minimum cardinality taken over all minimal connected dominating sets of GG. In this work, we characterize trees and unicyclic graphs with equal total domination and connected domination numbers.