On total and entire weightings of plane graphs and some special classes of graphs

• Main Authors: Ilagan, Mark Francis M., Velilla, Janelle Natalie L.
• Format: text
• Language: English
• Published: Animo Repository 2016
• Subjects: Graph theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/14907
• Institution: De La Salle University

This study discusses some results on entire weightings of plane graphs which induce proper vertex or proper face colorings. Specifically, entire weightings of 2-connected plane graphs are studied, and the minimum number of weights that make possible these proper vertex or face colorings are identified. This study also looks at total weightings of some classes of graphs which induce a proper vertex coloring. In particular, the minimum number of weights that can be used to generate a proper vertex coloring and graphs which admit a proper vertex coloring total weighting that uses at most two weights will be investigated. Most of the results in this paper are based on [12] and [16].