• GAUSSIAN PRIME LABELLING OF UNICYCLIC GRAPHS

Abstract

A graph G on n vertices is said to have a prime labelling if there exists a labelling from the vertices of G to the first n natural numbers such that any two adjacent vertices have relatively prime labels. Gaussian integers are the complex numbers whose real and imaginary parts are both integers. A Gaussian prime labelling on G is a bijection                   f: V (G) → [_n], the set of the first n Gaussian integers in the spiral ordering such that if uv ∈ E(G),then (u) and (v) are relatively prime. Using the order on the Gaussian integers, we discuss the Gaussian prime labelling of unicyclic graphs.