On Super Heronian Mean Labeling of Some Subdivision Graphs - Valencerina, Lorelie S.; Pedrano, Ariel C. (Communications in Mathematics and Applications, 2024)
Let \(f:V(G) \rightarrow \{1, 2, \dots, p+q \}\) 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,\[f^*(e)= \left \lfloor {\frac{f(u)+\sqrt{f(u)f(v)}+f(v)}{3}} \right \rfloor \ \text{or} \ \left \lceil\frac{f(u)+\sqrt{f(u)f(v)}+f(v)}{3} \right \rceil.\]Then \(f\) is called a super Heronian mean labeling if \(\{f(V(G))\} \cup \{f(e): e \in E(G)\}=\{1, 2, 3, \dots, p+q\}\). A graph which admits super Heronian mean labeling is called super Heronian mean graph.
Keywords: Super Heronian mean graph; Subdivision graph; Snake graphs