List-antimagic labeling of vertex-weighted graphs

A graph $G$ is $k$-$weighted-list-antimagic$ if for any vertex weighting $\omega\colon V(G)\to\mathbb{R}$ and list assignment $L\colon E(G)\to2^{\mathbb{R}}$ with $|L(e)|\geq |E(G)|+k$ there exists an edge labeling $f$ such that $f(e)\in L(e)$ all $e\in E(G)$, labels of edges are pairwise distinct, the sum on incident to a plus weight distinct from at every other vertex. In this paper we prove $n$ vertices having no $K_1$ or $K_2$ component $\lfloor{\frac{4n}{3}}\rfloor$-weighted-list-antimagic. An oriented $k$-$oriented-antimagic$ injective $E(G)$ into $\{1,\dotsc,|E(G)|+k\}$ toward minus away difference sums We admits orientation $\lfloor{\frac{2n}{3}}\rfloor$-oriented-antimagic.