On Total Edge Irregularity Strength of Some Graphs Related to Double Fan Graphs

Abstract

Let G = (V(G),E(G)) be a simple, connected, undirected graph with non empty vertex set V(G) and edge set E(G) . The function f : V(G) ∪ E(G) ↦ {1,2, ...,k} (for some positive integer k) is called an edge irregular total k −labeling where each two edges ab and cd , having distinct weights, that are f (a)+ f (ab)+ f (b) ≠ f (c)+ f (cd)+ f (d). The minimum k for which G has an edge irregular total k −labeling is denoted by tes (G) and called total edge irregularity strength of graph G . In this paper, we determine the exact value of the total edge irregularity strength of double fan ladder graph, centralized double fan graph, and generalized parachute graph with upper path.