The study of the b-choromatic number of some classes of fractal graphs


Sattar T., Sardar M. S. , Alaeiyan M., Farahani M. R. , Cancan M., Tas Z.

JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, vol.25, no.5, pp.1509-1524, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1080/09720529.2022.2067390
  • Journal Name: JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1509-1524
  • Keywords: b-coloring, b-choromatic number, Sierpinski graph, Sierpinski Gasket network, House graph, CHROMATIC NUMBER, METRIC DIMENSION, INDEXES, P(N
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In 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.