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On Domatic Number of Some Rotationally Symmetric Graphs

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  • Hassan Raza
  • Sunny Kumar Sharma
  • Muhammad Azeem
  • Gaetano Luciano

Abstract

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.

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  • Hassan Raza & Sunny Kumar Sharma & Muhammad Azeem & Gaetano Luciano, 2023. "On Domatic Number of Some Rotationally Symmetric Graphs," Journal of Mathematics, Hindawi, vol. 2023, pages 1-11, February.
    • Handle: RePEc:hin:jjmath:3816772
    DOI: 10.1155/2023/3816772
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    Cited by:

    1. Guruprakash Jayabalasamy & Cyril Pujol & Krithika Latha Bhaskaran, 2024. "Application of Graph Theory for Blockchain Technologies," Mathematics, MDPI, vol. 12(8), pages 1-45, April.

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