Grundy Chromatic Number of Shuriken Graphs and Applications to Regulatory Network Modeling

Authors

  • M. Kamalnath Kalasalingam Academy of Research and Education
  • Muthukani Vairavel T Kalasalingam Academy of Research and Education

DOI:

https://doi.org/10.19139/soic-2310-5070-3731

Keywords:

Grundy chromatic number, Shuriken graph, Line graph, Middle graph, Total graph, Gene regulatory networks, Graph coloring algorithms.

Abstract

The concept of Grundy coloring plays an important role in the study of graph coloring and its applications in sequential allocation problems. In this paper, we study the Grundy (first-fit) chromatic number of the Shuriken graph $Sh_n$ and some of its associated derived graphs obtained through standard graph operations. In particular, we determine the Grundy chromatic numbers of the line graph $L(Sh_n)$, the middle graph $M(Sh_n)$, and the total graph $T(Sh_n)$. The results are obtained by utilizing the structural properties of the Shuriken graph together with the principles of Grundy coloring and suitable upper bound techniques. In addition, we discuss the relevance of these graphs in the framework of Gene Regulatory Networks (GRNs), where the Grundy chromatic number may represent the maximum level of hierarchical activations arising in sequential regulatory interactions. Thus, the Shuriken graph and its related derived graphs provide meaningful mathematical models for studying interaction complexity and stability in biological systems.

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Published

2026-06-01

How to Cite

M. Kamalnath, & T, M. V. (2026). Grundy Chromatic Number of Shuriken Graphs and Applications to Regulatory Network Modeling. Statistics, Optimization & Information Computing, 16(1), 777–789. https://doi.org/10.19139/soic-2310-5070-3731

Issue

Vol. 16 No. 1 (2026)

Section

Research Articles

License

Copyright (c) 2026 M. Kamalnath, Muthukani Vairavel T

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