$b$-Local Irregular Chromatic Number of Graphs

  • Arika Indah Kristiana Universitas Jember
  • Ridho Alfarisi Department of Mathematics, Universitas Jember
  • Dafik Department of Mathematics Education, Universitas Jember
  • Sharifah Kartini Said Husain Department of Mathematics and Statistics, Universiti Putra Malaysia
  • N Mohanapriya Department of Mathematics, Kongunadu Arts and Science College, India
  • Witriany Basri Department of Mathematics and Statistics, Universiti Putra Malaysia
  • V. Ponsathya Department of Mathematics, Kongunadu Arts and Science College, India
DOI: https://doi.org/10.19139/soic-2310-5070-2759

Abstract

In this paper, we study a new notation of coloring of graph, namely a $b$-local irregularity coloring. Suppose $l : V(G) \rightarrow \{1,2, \ldots ,k\}$ is called vertex irregular $k$-labeling and $w : V(G) \rightarrow N$, where $w(u) = \sum_{v \in N(u)} l(v)$. Every color class has a representative adjacent to at least one vertex in each of the color classes.$l$ is $b$-local irregularity coloring. The $b$-local irregular chromatic number denoted by $\chi_{b-lis}(G)$ is the largest of $k$ such that $G$ admits a $b$-local irregularity coloring. In this paper, we study the $b$-local irregular chromatic number of graphs namely path, cycle, star, friendship, complete, complete bipartite, and Wheel graph.
Published
2025-10-26
How to Cite
Kristiana, A. I., Alfarisi, R., Dafik, Husain, S. K. S., Mohanapriya, N., Basri, W., & Ponsathya, V. (2025). $b$-Local Irregular Chromatic Number of Graphs. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2759
Issue
Online First
Section
Research Articles
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