On vertex irregular total labelings of cartesian products of two paths

Syed Ahtsham Ul Haq Bokhary, Ali Ahmad, M. Imran

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

A toted 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 cartesian and categorical product of two paths of given length.

Original languageEnglish
Pages (from-to)239-249
Number of pages11
JournalUtilitas Mathematica
Volume90
Publication statusPublished - Mar 2013
Externally publishedYes

Keywords

  • Cartesian products
  • Categorical product
  • Paths
  • Total vertex irregularity strength
  • Vertex irregular total k-labeling

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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