On super antimagicness of generalized flower and disk brake graphs (Q2831577)

A simple graph \(G=(V,E)\) is super \((a,d)\) anti-magic if there is a one-to-one mapping \(f : V \cup E \rightarrow \{1,2, \dots, |V|+|E| \}\) such that the edge weights \(w(uv)=f(u)+f(v) +f(uv)\) form an arithmetic sequence \(\{a, a+d, \dots, a+(|E|-1)d\}\), where \(a\geq 0\) and the smallest possible labels appear on the vertices. Antimagicness of generalized flower graphs as well as disk break graphs (these are special planar graphs of maximal valence 4) is constructively studied. Some open problems concerning super antimagicness of disjoint unions of these special graphs are formulated.