DisCoMath Seminar: How Symmetric is Your Graph?
DisCoMath Seminar
How Symmetric is Your Graph?
Dr. Brendan Rooney
School of Mathematics and Statistics
Rochester Institute of Technology
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Abstract:
A graph is asymmetric if its automorphism group is trivial. One measure of the symmetry of a graph ๐บ is the number of its edges need to be "changed'' in order to create an asymmetric graph (or the number of its edges need to be "changed'' to destroy all of its symmetries). We define the asymmetric index of ๐บ, denoted ๐๐(๐บ), to be the minimum value ๐+๐ so that adding some set of ๐ edges to ๐บ and deleting some set of ๐ edges from ๐บ results in an asymmetric graph. We present some results on asymmetric index, and consider asymmetric index for graphs that are "very'' symmetric.
Intended Audience:
All are Welcome!
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