5 problems

Let $G$ be a graph. A $D$-neighborhood of a vertex is the set of vertices at distance at most $D$ from it. Neighborhood characterization conjecture. A graph is $D$-distance antimag…

Let $G$ be a graph, let $D\subseteq\{0,1,2,\dots,\operatorname{diam}(G)\}$ be a non-empty distance set, and define the $D$-neighborhood of a vertex $u$ by … A bijection…

Let $G=(V,E)$ be an undirected simple graph. A bijection $h:V(G)\rightarrow\{1,2,\dots,|V(G)|\}$ is a distance antimagic labeling when the vertex weights … are distinct for all ver…

Kamatchi–Arumugam tree conjecture. $T$ is distance antimagic if and only if every support vertex $v$ has precisely one leaf adjacent to $v$.

Kamatchi–Arumugam conjecture. $G$ is distance antimagic if and only if $N(u)\ne N(v)$ for any two distinct vertices $u,v\in V(G)$.