Year: 2024
Type: article
Abstract: In the context of a simple undirected graph G G , a k k -prime labeling refers to assigning distinct integers from the set { k , k + 1 , … , ∣ V ( G ) ∣ + k − 1 } \left\{k,k+1,\ldots ,| V\left(G)| +k-1\right\} to its vertices, such that adjacent vertices in G G are labeled with numbers that are relatively prime to each other. If G G has a k k -prime labeling, we say that G G is a k k -prime graph ( k -PG). In this article, we characterize when a graph up to order 6 is a k -PG and characterize when a graph of order 7 is a k -PG whenever k k and k + 1 k+1 are not divisible by 5. Also, we find a lower bound for the independence number of a k -PG. Finally, we study when a cycle is a k -PG.
Source: Open Mathematics
Authors: Omar A. Abughneim, Baha’ Abughazaleh
Institutions: University of Jordan, Isra University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,082
OpenAlex ID: W4405114664