On a lower bound of connected domination number for graphs with prescribed degree sequence

We consider the lower bounds for the connected domination number yc(G) of the graph G. This can be defined as either the minimal cardinality of a dominating set of vertices inducing a connected subgraph of G, or as a minimal number of nonpendant vertices in a spanning tree of G. We obtain bounds on yc(G) for graphs with prescribed degree sequence. Our results imply, in particular, sharp bounds for regular graphs and some biregular graphs with leaves.