The pendant-vertex conjecture for local antimagic chromatic number of trees

Let $T_k$ be a tree with $k\ge 2$ pendant vertices. Caterpillars, spiders, and lobsters are standard classes of trees, and $\chi_{la}(T_k)$ denotes the local antimagic chromatic number of $T_k$. Pendant-vertex conjecture. Every tree $T_k$, other than certain caterpillars, spiders and lobsters, with $k\ge 2$ pendant vertices has $\chi_{la}(T_k)=k+1$. This proposes that the lower bound furnished by the pendant vertices is attained for all but specified exceptional tree families; the paper does not characterize the exceptional families or establish the assertion in general.