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Perfect colorings of patterns with multiple orbits
Author(s) -
Junio Allan,
Walo Ma. Lailani
Publication year - 2019
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273319011562
Subject(s) - mathematics , combinatorics , construct (python library) , complete coloring , computer science , graph , line graph , graph power , programming language
This paper studies colorings of patterns with multiple orbits, particularly those colorings where the orbits share colors. The main problem is determining when such colorings become perfect. This problem is attacked by characterizing all perfect colorings of patterns through the construction of sufficient and necessary conditions for a coloring to be perfect. These results are then applied on symmetrical objects to construct both perfect and non‐perfect colorings.