All Graphs of Order n with Distinguishing Number n−1 or n − 2 - Andi Pujo Rahadi; Edy Tri Baskoro; Suhadi Wido Saputro (Theory and Applications of Graphs)
Let G be a simple connected graph. The distinguishing number of G, denoted by D(G), is the least integer d such that G has a vertex d-labeling preserved only by the trivial automorphism. In this paper, we characterize all graphs of order n with distinguishing number n − 1, or n − 2.