Prime Labeling of Some Graphs with Eisenstein Integers
Korina Ernjulie Manaloto, Rovin B. Santos · SciEnggJ · 2023
A graph on n vertices is said to admit a prime labeling if the vertices can be labeled with the first n natural numbers in such a way that two adjacent vertices have relatively prime labels. In this paper, we define an order on the set of Eisenstein integers to extend the notion of prime labeling of graphs to the set of Eisenstein integers. Properties of the ordering are studied to come up with prime labelings of some families of graphs such as the flower, wheel, centipede, and double broom graphs.