The prime distance is a measure of the connectivity of a graph based on the concept of prime numbers. The Gaussian prime distance (GPD) graph G is defined as any graph with two relatively prime vertices. The Gaussian neighborhood prime distance (GNPD) graph is made up of a graph G and each vertex v, with neighboring vertices being relatively prime numbers. It is formed by dividing G into n separate Gaussian numbers such that adjacent vertex numbers are relatively prime numbers. The order in the XY plane was structured linearly by means of Gaussian integers to create a spiral structure and demonstrate that certain graph family have a finite Gaussian prime distance with the Gaussian integers.

Finite Gaussian Prime distance, Neighborhood Gaussian Prime Distance, Spiral order, Gaussian integers.