A Minimum Coprime Number for Amalgamation of Wheel

Abstract

Let 𝐺 be a simple graph of order 𝑛. A coprime labeling of a graph 𝐺 is a vertex labeling of 𝐺 with distinct positive integers from the set {1, 2, … , 𝑘} for some 𝑘 ≥ 𝑛 such that any adjacent labels are relatively prime. The minimum value of 𝑘 for which 𝐺 has a coprime labelling, denoted as 𝔭𝔯(𝐺), is called the minimum coprime number of 𝐺. A coprime labeling of 𝐺 with the largest label being 𝔭𝔯(𝐺) is said a minimum coprime labeling of 𝐺. In this paper, we give the exact value of the minimum coprime number for amalgamations of wheel 𝑊𝑛 when 𝑛 is odd positive integer