Trees with Distinguishing Number Three Andi Pujo Rahadi (a), Edy Tri Baskoro (b*), Suhadi Wido Saputro (c)
a), b), c) Center for Research Collaboration on Graph Theory and Combinatorics
a), b), c) Institut Teknologi Bandung
*ebaskoro[at]itb.ac.id
Abstract
Let G(V,E) be a simple connected graph with the vertex-set V and the edge-set E. A vertex k-labeling on G is a mapping f from V(G) onto {1,2,..., k}. The distinguishing number of G, denoted by D(G), is the least natural number k such that G has a vertex k-labeling that is preserved only by the trivial automorphism. In this talk, we characterize all trees of radius two with the distinguishing number three.
Keywords: distinguishing number- graph automorphism- tree
