Existence of local total neighborhood antimagic labelings

Establish that every graph admits a local total neighborhood antimagic labeling.

Background

A local total neighborhood antimagic labeling is a bijection from the vertices and edges of a graph to consecutive positive integers such that the induced neighborhood colors differ on every pair of adjacent vertices. Unlike ordinary antimagic labeling, equal induced colors are permitted for nonadjacent vertices.

The paper identifies universal existence as the central unresolved question for this labeling notion. The statement is made for every graph, without restricting to graphs already known to admit such a labeling.