Relationships between symmetry-based graph measures

This paper addresses the problem of comparing different measures of graph symmetry. Two measures, each based on the number and respective sizes of the vertex orbits of the automorphism group or a graph, are compared. A real valued distance measure is used to compare the symmetry measures by establishing the limiting value of the distances for several well known classes of graphs. (c) 2021 Elsevier Inc. All rights reserved.

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This paper compares two measures of graph symmetry based on the number and sizes of vertex orbits of the automorphism group, using a real valued distance measure to establish the limiting value of distances for several well-known classes of graphs.