Proof of a conjecture in domination theory

A dominating set D of a graph G is a least dominating set (l.d.s) if γ(〈D〉) ⩽ γ(〈D1〉) for any dominating set D1 (γ denotes domination number). The least domination number γ1(G) of G is the minimum cardinality of a l.d.s. We prove a conjecture of Sampathkumar (1990) that γ1 ⩽ 3p5 for any connected graph G of order p ⩾ 2.