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On reflexive edge strength of generalized prism graphs

Abstract:

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 has wt(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.