Gaussian Prime Labeling of Super Subdivision of Star Graphs

Abstract

Gaussian integers are the complex numbers of the form a + bi where $a, b \in Z$ and $i^{2} =-1$ and it is denoted by $ Z[i]$. A Gaussian prime labeling on G is a bijection from the vertices of G to $[\psi_{n}]$, the set of the first n Gaussian integers in the spiral ordering such that if $uv \in E(G)$, then $\psi(u)$ and $\psi(v)$ are relatively prime. Using the order on the Gaussian integers, we discuss the Gaussian prime labeling of super subdivision of star graphs.