Symmetry breaking in planar and maximal outerplanar graphs

الأصل · EN

The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has a vertex (edge) labeling with d 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 K₃, 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.