Abstract
Let <em>G = (V(G),E(G))</em> be a simple, connected, undirected graph with non empty vertex set <em>V(G)</em> and edge set<em> E(G)</em>. The function <em>f : V(G) ∪ E(G) ↦ </em>{1,2, ...,k} (for some positive integer k) is called an edge irregular total <em>k</em>−labeling where each two edges <em>ab</em> and<em> cd</em>, having distinct weights, that are<em> f (a)+ f (ab)+ f (b) ≠ f (c)+ f (cd)+ f (d).</em> The minimum <em>k</em> for which <em>G</em> has an edge irregular total <em>k</em>−labeling is denoted by tes<em>(G)</em> and called total edge irregularity strength of graph <em>G</em>. 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.
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