Sattar, TayyibaSardar, Muhammad ShoaibAlaeiyan, MehdiFarahani, Moahmmad RezaCancan, MuratTas, Ziyattin2025-05-102025-05-1020220972-05292169-006510.1080/09720529.2022.20673902-s2.0-85132772546https://doi.org/10.1080/09720529.2022.2067390https://hdl.handle.net/20.500.14720/14169Alaeiyan, Mehdi/0000-0003-2185-5967; Shoaib Sardar, Muhammad/0000-0001-7146-5639In graph coloring, labels are assigned to graph elements according to certain constraints. Colors are a special case of graph labeling as well as in practical applications, graph coloring also poses some theoretical challenges. A topic related to graph coloring will be discussed in this study, i.e., b-chromatic number. In proper coloring, edges, vertices, or both of them are colored so that they are distinct from one another. A b-coloring of m colors of a graph G is similar to proper coloring in which at least one vertex from each color class is connected to (m-1) other colors. The b-chromatic number of a graph G is the greatest positive number k such that G admits a b-coloring with k colors and is represented by phi(G). Fractals are geometric objects that are self-similar at multiple scales and their geometric measurements are different from fractal measurements. In this paper, we will evaluate the b-chromatic number of Fractal type graphs, i.e., Sierpinski network S(n; Kk) (where Kk is a complete graph of order k) and Sierpinski gasket network S(n). Firstly, we will compute the b-chromatic number of S(n; K3), S(n; K4) and S(n; K5) for n >= 2. After that, we will generalize the result for the Sierpinski network of complete graph Kk. In addition, we will also determine the b-choromatic number of Sierpinski gasket graph S(n). As an application, we will also determine the b-chromatic number of Sierpinski graph of house graph.eninfo:eu-repo/semantics/closedAccessB-ColoringB-Choromatic NumberSierpinski GraphSierpinski Gasket NetworkHouse GraphArticle255N/AQ215091524WOS:000814112400001