Total vertex irregularity strength of disjoint union of helm graphs

Ali Ahmad, E. T. Baskoro, M. Imran

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2, . . . , k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G. We have determined an exact value of the total vertex irregularity strength of disjoint union of Helm graphs.

Original languageEnglish
Pages (from-to)427-434
Number of pages8
JournalDiscussiones Mathematicae - Graph Theory
Volume32
Issue number3
DOIs
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Helm graphs
  • Total vertex ir- regularity strength
  • Vertex irregular total k-labeling

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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