NILAI KETAKTERATURAN SISI TOTAL PADA GRAF AMALGAMASI SUBDIVISI GRAF DOVETAIL

  • Eka Nurdini Universitas Negeri Semarang
  • Isnaini Rosyida Universitas Negeri Semarang
  • Mulyono Mulyono Universitas Negeri Semarang
Keywords: Irregular total labeling, Graph labeling, irregularity strength, total edge irregularity strength, dovetail graphs.

Abstract

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, w(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 Amalgamation between Subdivision of Dovetail graph with pendant vertices and cycle graph (〖SD〗_n^n,x)*(C_(3n-3),z). The results of this research are tes((〖SD〗_n^n,x)*(C_(3n-3),z))=⌈(9n-3)/3⌉.

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Published
2020-06-22
Section
Articles