Algorithm to Construct Graph with Total Vertex Irregularity Strength Two

Denny Riama Silaban, Hikmatiarahmah Kekaleniate, Siti Lutpiah, Kiki Ariyanti, Edy Tri Baskoro

Research output: Contribution to journalConference articlepeer-review

Abstract

A total vertex irregularity strength of a graph G, tvs(G), is the minimum positive integer k such that there is a mapping f from the union of vertex and edge sets of G to {1, 2, ⋯, k} and the weights of all vertices are distinct. The weight of a vertex in G is the sum of its vertex label and the labels of all edges that incident to it. It is known that tvs(Kn) = 2. In this paper, we construct graphs with tvs equal to 2 by removing as much as possible edges from Kn, with and without maintaining the outer cycle Cn of Kn. To do so, we give two algorithms to construct the graphs, and show that the tvs of the resulting graph is equal to 2.

Original languageEnglish
Pages (from-to)132-137
Number of pages6
JournalProcedia Computer Science
Volume74
DOIs
Publication statusPublished - 1 Jan 2015
Event2nd International Conference of Graph Theory and Information Security, 2015 - Bandung, Indonesia
Duration: 21 Sep 201523 Sep 2015

Keywords

  • algorithm
  • complete graph
  • cycle
  • Total vertex irregularity strength

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