On reflexive edge strength of generalized prism graphs

Muhammad Irfan (University of Okara, Okara, Pakistan)
Martin Baca (Department of Applied Mathematics and Informatics, Technical University, Ko\v{s}ice, Slovak Republic)
Andrea Semanicova-Fenovcikova (Department of Applied Mathematics and Informatics, Technical University, Ko\v{s}ice, Slovak Republic)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications

Let G be a connected, simple and undirected graph. The assignments {0, 2, …, 2kv} to the vertices and {1, 2, …, ke} to the edges of graph G are called total k-labelings, where k = max{ke, 2kv}. The total k-labeling is called an reflexive edge irregular k-labeling of the graph G, if for every two different edges xy and x′y′ of G, one haswt(xy)=fv(x)+fe(xy)+fv(y)≠wt(x′y′) = fv(x′) + fe(x′y′) + fv(y′).The minimum k for which the graph G has an reflexive edge irregular k-labeling is called the reflexive edge strength of G. In this paper we investigate the exact value of reflexive edge strength for generalized prism graphs.