On Domatic Number of Some Rotationally Symmetric Graphs
Domination is a well-known graph theoretic concept due to its significant real-world applications in several domains, such as design and communication network analysis, coding theory, and optimization. For a connected graph Γ=V,E, a subset U of VΓ is called a dominating set if every member present in V-U is adjacent to at least one member in U. The domatic partition is the partition of the vertices VΓ into the disjoint dominating set. The domatic number of the graph Γ is the maximum cardinality of the disjoint dominating sets. In this paper, we improved the results for the middle and central graphs of a cycle, respectively. Furthermore, we discuss the domatic number for some other cycle-related graphs and graphs of convex polytopes.
Journal of Mathematics
Raza, Hassan; Sharma, Sunny Kumar; and Azeem, Muhammad, "On Domatic Number of Some Rotationally Symmetric Graphs" (2023). Kean Publications. 425.