Reflexive edge strength of convex polytopes and corona product of cycle with path - Yoong, Kooi-Kuan; Hasni, Roslan; Lau, Gee-Choon; Asim, Muhammad Ahsan; Ahmad, Ali (AIMS mathematics, 2022)
For a graph $ G $, we define a total $ k $-labeling $ φ $ is a combination of an edge labeling $ φ_e(x)→\{1, 2, …, k_e\} $ and a vertex labeling $ φ_v(x) → \{0, 2, …, 2k_v\} $, such that $ φ(x) = φ_v(x) $ if $ x\in V(G) $ and $ φ(x) = φ_e(x) $ if $ x\in E(G) $, then $ k = \, max\, \{k_e, 2k_v\} $. The total $ k $-labeling $ φ $ 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 $ \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.