Calculating The Star Chromatic Number for Jahangir Graphs And Limon Graphs

Abstract

The field of graph coloring has witnessed notable interest, particularly with the introduction of new conditions and constraints that increase the complexity of the problem and broaden its diverse applications in computer science and network theory. Among the most prominent types of coloring are distance coloring with distance 2 [2], star coloring [3,5], and acyclic coloring [7,5], which requires that the graph be free of bi-chromatic cycles. These studies reflect the importance of the graph coloring problem as an applied research area.

This paper focuses on star coloring (coloring without bi-chromatic  paths). Attention is given to specific classes of graphs, and the values of the star chromatic number  are determined for some of these graphs. In particular, the star chromatic number  is computed for Jahangir graphs , Lemon graphs, and the Firecracker graph  in the case .