Realizations of automorphism groups of metric graphs induced by rational maps
Song JuAe

TL;DR
This paper explores how automorphism groups of metric graphs can be realized via rational maps into tropical projective spaces, linking graph symmetries with tropical linear groups.
Contribution
It provides a method to realize automorphism groups of metric graphs as subgroups of tropical linear groups through rational maps.
Findings
Automorphisms induce permutations of coordinates in tropical projective space.
Automorphism groups can be embedded into tropical linear groups.
The approach connects graph symmetries with tropical algebraic structures.
Abstract
For a rational map from a metric graph to a tropical projective space defined by a ratio of rational functions , an automorphism of induces a permutation of the coordinates of if is -invariant. Through this description, we can realize the automorphism group of as ambient automorphism group such as tropical projective general linear group, tropical general linear group and -linear transformation group of Euclidean space.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Control and Dynamics of Mobile Robots · Advanced Topics in Algebra
