Article ID Journal Published Year Pages File Type
4648214 Discrete Mathematics 2012 19 Pages PDF
Abstract

A graph GG is said to be dd-distinguishable   if there is a labeling c:V(G)→{1,2,…,d}c:V(G)→{1,2,…,d} such that no automorphism of GG other than the identity map preserves the labels of vertices given by cc. The smallest dd for which GG is dd-distinguishable is called the distinguishing number   of GG. We shall prove that every 4-representative triangulation on a closed surface, except the sphere, is 2-distinguishable after establishing a general theorem on the distinguishability of polyhedral graphs faithfully embedded on closed surfaces, and show that there is an upper bound for the distinguishing number of triangulations on a given closed surface, applying the re-embedding theory of triangulations.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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