An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is local antimagic if vertex-weights are distinct for pair neighboring vertices, where vertex-weight sum labels all edges incident with that vertex. Any induces proper vertex coloring G color its vertex-weight. This naturally leads to concept chromatic number. The number defined be minimum colors take...

The chromatic vertex (resp. edge) stability number vsχ(G) esχ(G)) of a graph G is the minimum vertices edges) whose deletion results in H with χ(H)=χ(G)−1. In main result it proved that if χ(G)∈{Δ(G),Δ(G)+1}, then vsχ(G)=ivsχ(G), where ivsχ(G) independent number. need not hold for graphs χ(G)≤Δ(G)+12. It χ(G)>Δ(G)2+1, vsχ(G)=esχ(G). A Nordhaus–Gaddum-type on also given.