Radio Heronian mean labeling of some Corona related graphs

Abstract

A radio heronian mean labeling of a connected graph $\mathrm{G}$ is a one to one map $\mathrm{g}$ from the vertex set $V(G)$ to the set of natural numbers $N$ such that for any two distinct vertices $s$ and $t$ of $G, d(s, t)+\left\lceil\frac{g(s)+g(t)+\sqrt{g(s) g(t)}}{3}\right\rceil \geq 1+D$, where $D$ is the diameter of $G$. The radio heronian mean number of $\mathrm{g}, r h m n(\mathrm{~g})$, is the maximum number assigned to any vertex of G. The radio heronian mean number of $\mathrm{G}, \operatorname{rhmn}(G)$, is the minimum value of $\operatorname{rhmn}(\mathrm{g})$, taken overall radio heronian mean labelings $\mathrm{g}$ of $\mathrm{G}$. In this paper, we investigate the radio heronian mean number of $T_n \odot K_1, I T_n \odot K_1$ and $Q_n \odot K_1$.