1 research outputs found
Symmetry breaking in planar and maximal outerplanar graphs
The distinguishing number (index) () of a graph is the
least integer such that has a vertex (edge) labeling with labels
that is preserved only by a trivial automorphism. In this paper we consider the
maximal outerplanar graphs (MOP graphs) and show that MOP graphs, except ,
can be distinguished by at most two vertex (edge) labels. We also compute the
distinguishing number and the distinguishing index of Halin and Mycielskian
graphs.Comment: 10 pages, 6 figure