Prime Labeling of Some Graphs with Eisenstein Integers

Manaloto, Korina Ernjulie T.; Santos, Rovin B.

VOLUME 16 NUMBER 2 (July to December 2023)

PSL%202021 vol14-no01-p12-28-Mikita%20and%20Padlan

SciEnggJ. 2023 16 (2) 329-336
available online: September 30, 2023

*Corresponding author
Email Address: rbsantos8@up.edu.ph
Date received: May 30, 2023
Date revised: July 31, 2023
Date accepted: August 1, 2023

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ARTICLE

Prime Labeling of Some Graphs with Eisenstein Integers

Korina Ernjulie T. Manaloto and Rovin B. Santos*

Institute of Mathematics, College of Science, University of the Philippines,
Diliman, Quezon City, 1101, Philippines

KEYWORDS: graph labeling, prime labeling, eisenstein integers, trees, graphs

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.