On Super Heronian Mean Labeling of Some Subdivision Graphs - Valencerina, Lorelie S.; Pedrano, Ariel C. (Communications in Mathematics and Applications, 2024)
Let \(f:V(G) → {1, 2, …, p+q }\) be an injective function, where \(p=|V(G)|\) and \(q=|E(G)|\). For a vertex labeling \(f\) the induced edge labeling \(f^*(e=uv)\) is defined by, \[ f^*(e)= f(u)+f(u)f(v)+f(v)3 floor or f(u)+f(u)f(v)+f(v)3 ceil. \] Then \(f\) is called a super Heronian mean labeling if \({f(V(G))} {f(e): e E(G)}={1, 2, 3, …, p+q}\). A graph which admits super Heronian mean labeling is called super Heronian mean graph.