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August 14, 2025Journal of the Indonesian Mathematical Society0 citationsOpen Access

Diachromatic Number of Some Acyclic Digraphs

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RRRaventino RaventinoYSYeni Susanti

Key Points

  • The maximum number of colors needed for complete coloring in specific acyclic digraphs varies significantly.
  • This study addresses diachromatic numbers across four types of digraphs—lobster, fireworks, banana tree, and coconut tree digraphs.
  • The analysis involves both specified and arbitrary directional orientations of the digraphs.
  • Understanding these characteristics may inform broader applications in graph theory and related fields.

Abstract

A vertex coloring that ensures every pair of different colors is represented at least once is termed complete coloring. The diachromatic number of an acyclic digraph denotes the maximum number of colors required for its complete coloring. This study delves into the diachromatic numbers of lobster digraphs, fireworks digraphs, banana tree digraphs, and coconut tree digraphs under specific and arbitrary directional orientations.

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Cite This Study

Raventino et al. (2025) studied this question.

synapsesocial.com/papers/68af4cdfad7bf08b1ead64fchttps://doi.org/10.22342/jims.v31i3.1710
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Zykov sums of digraphs with diachromatic number equal to its harmonious number2024
  2. 2On the minimum number of arcs in 4‐dicritical oriented graphs2024
  3. 3A Note on Acyclic Coloring of Strong Product of Graphs2024 · 2 citations
  4. 4Minimum acyclic number and maximum dichromatic number of oriented triangle-free graphs of a given order2024
  5. 5Arc-distinguishing of orientations of graphs2024