4−Equitable Tree Labelings
Zena Charlie Coles, Alana Huszar, Jared Miller, Zsuzsanna Szaniszló · ValpoScholar (Valparaiso University) · 2017
We assign the labels {0,1,2,3} to the vertices of a graph; each edge is assigned the absolute difference of the incident vertices’ labels. For the labeling to be 4−equitable, we require the edge labels and vertex labels to each be distributed as uniformly as possible. We study 4−equitable labelings of different trees and prove all cater-pillars, symmetric generalized n−stars (or symmetric spiders), and complete n −ary trees for all n ∈ N are 4−equitable.