b-Local Irregular Chromatic Number of Graphs - Kristiana, Arika Indah; Husain, Sharifah Kartini Said; Mohanapriya, N; Alfarisi, Ridho; Dafik; Basri, Witriany; Ponsathya, V. (Statistics, Optimization & Information Computing, 2025)
In this paper, we study a new notation of coloring of graph, namely a b-local irregularity coloring. Suppose l : V(G) → {1,2, … ,k} is called vertex irregular k-labeling and w : V(G) → N, where w(u) = _v 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 χ_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.