On b-chromatic Number of Prism Graph Families

Authors

Nadeem Ansari, IES, IPS Academy
R. S. Chandel, Govt. Geetanjali Girls College
Rizwana Jamal, Saifia Science College

Abstract

A b-coloring of graph 𝐺 is a proper 𝑘-coloring 𝐶 that verifies the following property: for every color class 𝑐𝑖, 1≤𝑖≤𝑘, there exists a vertex 𝑥𝑖, with color 𝑐𝑖, such that all the other colors in 𝐶 are utilized in 𝑥𝑖 neighbors. The b-chromatic number of a graph 𝐺, denoted by 𝜑(𝐺), is the largest integer 𝑘 such that 𝐺 may have a b-coloring by 𝑘 colors. In this paper we discuss the b-coloring of prism graph 𝑌𝑛, central graph of prism graph 𝐶(𝑌𝑛), middle graph of prism graph 𝑀(𝑌𝑛) and the total graph of prism graph 𝑇(𝑌𝑛) and we obtain the b-chromatic number for these graphs.

Recommended Citation

Ansari, Nadeem; Chandel, R. S.; and Jamal, Rizwana (2018). On b-chromatic Number of Prism Graph Families, Applications and Applied Mathematics: An International Journal (AAM), Vol. 13, Iss. 1, Article 20.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss1/20