On Super Heronian Mean Labeling of Subdivision Graphs

Abstract

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,
$$f^*(e)= \left \lfloor {\frac{f(u)+\sqrt{f(u)f(v)}+f(v)}{3}} \right \rfloor \ or \ \left \lceil\frac{f(u)+\sqrt{f(u)f(v)}+f(v)}{3} \right \rceil.$$
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.