Local Distance Antimagic Labeling of Neighborhood Balanced Colored Graphs

Let $G=(V,E)$ be a graph without isolated vertices. A bijection $f\colon V\to \{1,2,\dots,|V|\}$ is called a local distance antimagic labeling if $w(u)\not=w(v)$ for every edge $uv\in E$, where the weight $w(u)$ of a vertex $u$ is defined as the sum of labels assigned to all vertices adjacent to $u$