The paper addresses the question of Choi, Hartke, and Kaule as to whether there are graphs for which the distinguishing chromatic number is near the chromatic number.
📌 3 Key Takeaways
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Objective & Hypothesis:The distinguishing chromatic number $\chi_D(G)$ of a graph $G$ is the smallest number of colors needed to properly color the vertices of $G$ such that the only automorphism of $G$ that preserves colors is the identity.
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Key Findings & Data:Studying the distinguishing chromatic number of graphs produced some interesting work, and in continuation, we may prefer toinvestigate the distinguishing chromatic number of the hierarchical product of graphs.
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Conclusion & Impact:The paper addresses the question of Choi, Hartke, and Kaule as to whether there are graphs for which the distinguishing chromatic number is near the chromatic number.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:chromatic number · distinguishing chromatic number · graph automorphism
Abstract
The distinguishing chromatic number $\chi_D(G)$ of a graph $G$ is the smallest number of colors needed to properly color the vertices of $G$ such that the only automorphism of $G$ that preserves colors is the identity. Studying the distinguishing chromatic number of graphs produced some interesting work, and in continuation, we may prefer toinvestigate the distinguishing chromatic number of the hierarchical product of graphs. The paper addresses the question of Choi, Hartke, and Kaule as to whether there are graphs for which the distinguishing chromatic number is near the chromatic number.
Amouzegar, T., Khashyarmanesh, K. (2026). Distinguishing chromatic number of the hierarchical product of graphs. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 2. https://doi.org/10.15672/hujms.1215743
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