Bounding the domination number of a tree in terms of its annihilation number

A set S of vertices in a graph G is a dominating set if every‎ ‎vertex of V-S is adjacent to some vertex in S‎. ‎The domination‎ ‎number \gamma(G) is the minimum cardinality of a dominating set‎ ‎in G‎. ‎The annihilation number a(G) is the largest integer k‎ ‎such that the sum of the first k terms of the non-decreasing‎ ‎degree sequence of G is at most the number of edges in G‎. ‎In‎ ‎this paper‎, ‎we show that for any tree T of order n\ge ۲‎, ‎\gamma(T)\le \frac{۳a(T)+۲}{۴}‎, ‎and we characterize the trees‎ ‎achieving this bound‎.

Keywords:

annihilation number , dominating set , Domination Number