Construction of tropical morphisms from tropical modifications of nonhyperelliptic genus 3 metric graphs with tree gonality 3 to metric trees

In this article, we look into the tree gonality of genus $3$ metric graphs $Γ$ which is defined as the minimum of degrees of all tropical morphisms from any tropical modification of $Γ$ to any metric tree. It is denoted by tgon$(Γ)$ and is at most $3$. We define hyperelliptic metric graphs in terms