On Computing the Distinguishing Numbers of Planar Graphs and Beyond: a Counting Approach

A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest integer k for which G has a distinguishing k-labeling. In this paper, we apply the principle of inclusion-exclusion and develop recursive formulas to count the number of inequivalent distinguishing k-labelings of a graph. Along the way, we prove that the distinguishing number of a planar graph can be computed in time polynomial in the size of the graph.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Vikraman Arvind, Christine T. Cheng, Nikhil R. Devanur
• Keywords: CORR 2007, Education, Identity Map, Inequivalent Distinguishing K-labelings, Smallest Integer