The R-dynamic local irregularity vertex coloring of graph

Arika Indah Kristiana, Moh Imam Utoyo, Dafik, Ridho Alfarisi, Eko Waluyo

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We define the r-dynamic local irregularity vertex coloring. Suppose λ: V(G) → {1,2, …, k} is called vertex irregular k-labeling and w: V(G) → N where (formula presented). λ is called r-dynamic local irregular vertex coloring, if: (i) opt(λ) = min{max{λi}; λi vertex irregular k-labeling}, (ii) for every uv Є E(G), w(u) ≠ w(v), and (iii) for every v Є V(G) such that |w(N(v))| ≥ min{r, d(v)}. The chromatic number r-dynamic local irregular denoted by (formula presented), is minimum of cardinality r-dynamic local irregular vertex coloring. We study the r-dynamic local irregularity vertex coloring of graph and we have found the exact value of chromatic number r-dynamic local irregularity of some graph.

Original languageEnglish
Pages (from-to)767-769
Number of pages3
JournalInternational Journal of Scientific and Technology Research
Volume8
Issue number7
Publication statusPublished - Jul 2019

Keywords

  • Local irregularity
  • R-dynamic coloring
  • Vertex coloring

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