Total Edge Irregularity Strength of the Disjoint Union of Helm Graphs

Muhammad Kamran Siddiqui¹, Nurdin² & Edy Tri Baskoro^3
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.