On total irregularity strength of star graphs, double-stars and caterpillar

Diari Indriati, Widodo, Indah E. Wijayanti, Kiki Ariyanti

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Citations (Scopus)

Abstract

For a simple graph G = (V, E) with the vertex set V and the edge set E, a totally irregular total k-labeling f: V U E → {1, 2,..., k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x', their weights wt f(x) = f(x) + Σxy∈E f (xy) and wtf (x') = f (x') + Σx' y' ∈E f (x'y') are distinct, and for any two different edges xy and x'y' their weights f (x) + f (xy) + f (y) and f (x') + f (x'y') + f (y') are also distinct. A total irregularity strength of graph G, denoted by ts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for star graphs, double stars and caterpillar.

Original languageEnglish
Title of host publicationProceedings of the 7th SEAMS UGM International Conference on Mathematics and Its Applications 2015
Subtitle of host publicationEnhancing the Role of Mathematics in Interdisciplinary Research
EditorsYeni Susanti, Indah Emilia Wijayanti, Fajar Adi Kusumo, Irwan Endrayanto Aluicius
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413542
DOIs
Publication statusPublished - 11 Feb 2016
Event7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research - Yogyakarta, Indonesia
Duration: 18 Aug 201521 Aug 2015

Publication series

NameAIP Conference Proceedings
Volume1707
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research
CountryIndonesia
CityYogyakarta
Period18/08/1521/08/15

Keywords

  • caterpillar
  • double stars
  • star
  • total irregularity strength
  • totally irregular total k-labeling

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