Trees with distinguishing index equal distinguishing number plus one

Saeid Alikhani, Sandi Klavžar, Florian Lehner, Samaneh Soltani

Research output: Contribution to journalArticlepeer-review


The distinguishing number (index)D(G) (D′(G)) of a graphGis theleast integerdsuch thatGhas an vertex (edge) labeling withdlabels thatis preserved only by the trivial automorphism. It is known that for everygraphGwe haveD′(G)≤D(G) + 1. In this note we characterize finite treesfor which this inequality is sharp. We also show that ifGis a connectedunicyclic graph, thenD′(G) =D(G)
Original languageEnglish
Pages (from-to)875-884
Number of pages10
JournalDiscussiones Mathematicae Graph Theory
Issue number3
Publication statusPublished - 2020

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