Reflexive edge strength of convex polytopes and corona product of cycle with path

For a graph $G$, we define a total $k$-labeling $\phi$ is a combination of an edge labeling ${\phi }_e(x)\to \{1,2,\dots ,k_e\}$ and a vertex labeling ${\phi }_v(x)\to \{0,2,\dots ,2k_v\}$, such that $\phi (x)={\phi }_v(x)$ if $x\in V(G)$ and $\phi (x)={\phi }_e(x)$ if $x\in E(G)$, then $k=\text{max}\{k_e,2k_v\}$. The total $k$-labeling $\phi$ is an edge irregular reflexive $k$-labeling of $G$ if every two different edges $xy$ and $x^{\mathrm{\prime }}{y}^{\mathrm{\prime }}$, the edge weights are distinct. The smallest value $k$ for which such labeling exists is called a reflexive edge strength of $G$. In this paper, we focus on the edge irregular reflexive labeling of antiprism, convex polytopes ${\mathcal{D}}_n$, ${\mathcal{R}}_n$, and corona product of cycle with path. This study also leads to interesting open problems for further extension of the work.