Trees with distinguishing index equal distinguishing number plus oneAlikhani, Saeid (Avtor) Klavžar, Sandi (Avtor) Lehner, Florian (Avtor) Soltani, Samaneh (Avtor) automorphism groupdistinguishing indexdistinguishing numbertreeunicyclic graphThe distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism. It is known that for every graph G we have D'(G) \leq D(G) + 1. In this note we characterize finite trees for which this inequality is sharp. We also show that if G is a connected unicyclic graph, then D'(G) = D(G).Technical University Press20202025-03-11 08:26:19Znanstveno delo92004sl