On reflexive edge strength of generalized prism graphs

Abstract

Let G be a connected, simple and undirected graph. The assignments {0, 2, . . . , 2k v } to the vertices and {1, 2, . . . , k e } to the edges of graph G are called total k-labelings, where k = max{k e , 2k v }. 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 has wt(xy) = f v (x) + f e (xy) + f v (y) = wt(x y ) = f v (x ) + f e (x y ) + f v (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.