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On total edge irregularity strength of some graphs related to double fan graphs. (English) Zbl 1463.42010

Summary: 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 \(f : V(G) \cup E(G) \mapsto \{1, 2, \ldots, k\}\) (for some positive integer \(k\)) is called an edge irregular total \(k-\)labeling where each two edges aband cd, having distinct weights, that are \(f(a)+ f(ab)+ f(b) \neq f(c)+ f(cd)+ f(d)\). 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.

MSC:

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42C15 General harmonic expansions, frames
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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