• GAUSSIAN PRIME LABELLING OF UNICYCLIC GRAPHS

RAJESH KUMAR T.J, MATHEW VARKEY T.K

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.


Keywords


Gaussian integers, Gaussian prime labelling, unicyclic graphs.

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