The exceptional-graph conjecture for local antimagic chromatic number

Let $G$ be a graph with $k\ge 1$ pendant vertices and chromatic number $\chi(G)$ satisfying $k\ge \chi(G)-1$. The graphs $K(2;a,b)$, caterpillar graphs in the cited theorem, $Ct(3;n_1,0,n_3)$, and the indicated corona graphs $P_m\odot O_n$, $C_m\odot O_n$, and $K_m\odot O_n$ are defined by the displayed exceptional conditions. Exceptional-graph conjecture. All graphs $G$ with $k\ge\chi(G)-1$ pendants have $\chi_{la}(G)=k+1$, except the following cases: $\chi_{la}(K(2;a,b))=a+b+2$ for $a\ge b\ge2$ and $a<b(b+1)/2$; the caterpillar graphs in Theorem~; $\chi_{la}(Ct(3;n_1,0,n_3))=n_1+n_3+2$ under the stated inequalities and congruence condition; and the three stated corona families with their displayed values or lower bound. This is presented as a proposed global classification; no resolution is supplied in the paper.