Abstract
For a graph G, we define a total k-labeling so is a combination of an edge labeling phi(e)(x) -> (1, 2, ... ,k(e)) and a vertex labeling phi(nu)(x) (0, 2, ...,2k(nu)), such that phi(x) = phi(nu)(x) if x is an element of V(G) and phi(x) = phi(e)(x) if x is an element of E(G), then k = max (k(e), 2k(nu)). The total k-labeling cc is an edge irregular reflexive k-labeling of G if every two different edges xy and x'y', 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 D-u, R-n, and corona product of cycle with path. This study also leads to interesting open problems for further extension of the work.