Incidence coloring of Regular graphs and Complement graphs
Pak Kiu Sun

TL;DR
This paper explores the conditions under which regular graphs can be incidence colored with a specific number of colors and establishes optimal inequalities relating to their incidence chromatic number.
Contribution
It provides necessary and sufficient conditions for r-regular graphs to be (r+1)-incidence colorable and determines the optimal Nordhaus-Gaddum inequality for the incidence chromatic number.
Findings
Characterization of r-regular graphs that are (r+1)-incidence colorable
Optimal Nordhaus-Gaddum inequality for incidence chromatic number
Relation between domination number and incidence chromatic number
Abstract
Using a relation between domination number and incidence chromatic number, we obtain necessary and sufficient conditions for -regular graphs to be -incidence colorable. Also, we determine the optimal Nordhaus-Gaddum inequality for the incidence chromatic number.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · graph theory and CDMA systems
