The local total antimagic bound for graphs with few pendant edges

Let $G$ be a graph with $k$ pendant edges, let $\Delta(G)$ be its maximum degree, and let $\chi_{lt}(G)$ denote its local total antimagic chromatic number. Local total antimagic bound conjecture. If $k\leq\Delta(G)$, then

$$\Delta(G)+1\leq\chi_{lt}(G)\leq\Delta(G)+2.$$

The conjecture is motivated by the known results summarized in the paper; whether these bounds hold for every such graph remains open.