On total edge irregularity strength of dove tail graph with pendant vertices and its subdivision

• Published in: Journal of physics. Conference series 2019-05, Vol.1217 (1), p.12064
• Main Authors: Nurdini, E, Rosyida, I
• Format: Article
• Language: English
• Subjects: Apexes; Graph theory; Irregularities; Labeling; Labels; Physics; Weight
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1217/1/012064

Given a graph G(V, E) with a non-empty set V of vertices and a set E of edges. A total labelling λ: V ∪ E → { 1, 2,. . ., k} is called an edge irregular total labelling if the weight of every edge is distinct. The weight of an edge e, under the total labelling λ, is the sum of label of edge e and all labels of vertices that are incident to e. In other words, wt(xy) = λ(xy) + λ(x) + λ(y). The total edge irregularity strength of G, denoted by tes(G) is the minimum k used to label graph G with the edge irregular total labelling. In this paper, authors investigate the total edge irregularity strength of Dove tail graph with n pendant vertices D n n , and the subdivision of D n n which is denoted as SD n n . The results of this research are t e s ( D n n ) = ⌈ 3 n + 1 3 ⌉ and t e s ( SD n n ) = ⌈ 6 n 3 ⌉ .