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Total Edge Irregularity Strength of the Disjoint Union of Helm Graphs
Muhammad Kamran Siddiqui1, Nurdin2 & Edy Tri Baskoro3
1Abdus Salam School of Mathematical Sciences,
68-B New Muslim Town, GC University, Lahore, Pakistan
2Mathematics Department, Faculty of Mathematics, and Natural Sciences, Hasanuddin University, Jalan Perintis Kemerdekaan, Km.10 Tamalanrea, Makassar, Indonesia
3Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa No. 10. Bandung 40132, Indonesia
Email: kamransiddiqui75@gmail.com
Abstract. The total edge irregular k-labeling of a graph G=(V,E) is the labeling of vertices and edges of G in such a way that for any different edges their weights are distinct. The total edge irregularity strength, tes (G), is defined as the minimum k for which G has a total edge irregular k-labeling. In this paper, we consider the total edge irregularity strength of the disjoint union of m special types of helm graphs.
Keywords: disjoint union; edge irregular total labeling; helm graph; irregularity strength; total edge irregularity strength.
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