The Construction of Labeling and Total Irregularity Strength of Specified Caterpillar Graph

Diari Indriati, Widodo, Isnaini Rosyida, Kiki Ariyanti

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)

Abstract

Let G be a simple, connected and undirected graph with vertex set V and edge set E. A total k-labeling f : V ∪ E → {1, 2, ⋯, k} is defined as totally irregular total k-labeling if the weights of any two different both vertices and edges are distinct. The weight of vertex x is defined as wt(x) = f(x) + ∑xy∈E f(xy), while the weight of edge xy is wt(xy) = f(x) + f(xy) + f(y). A minimum k for which G has totally irregular total k-labeling is mentioned as total irregularity strength of G and denoted by ts(G). This paper contains investigation of totally irregular total k-labeling for caterpillar graphs Sn,2,m and determination of their total irregularity strengths. In addition, the total vertex and total edge irregularity strength of this graph also be determined. The results are tvs(Sn;2;m) = ⌈n+m-1/2⌉, tes(Sn;2;m) =⌈n+m+2/3⌉ and ts(Sn;2;m) = ⌈n+m-1/2⌉for n, m ≥ 3.

Original languageEnglish
Article number012018
JournalJournal of Physics: Conference Series
Volume855
Issue number1
DOIs
Publication statusPublished - 12 Jun 2017
Event1st International Conference on Mathematics: Education, Theory, and Application, ICMETA 2016 - Surakarta, Indonesia
Duration: 6 Dec 20167 Dec 2016

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