• SKOLEM DIFFERENCE FIBONACCI MEAN LABELLING OF SOME STANDARD GRAPHS

Abstract

The concept of Skolem difference mean labelling was introduced by K. Murugan and A. Subramanian [6]. The concept of Fibonacci labelling was introduced by David W. Bange and Anthony E. Barkauskas [1] in the form Fibonacci graceful. This motivates us to introduce Skolem difference Fibonacci mean labelling and is defined as follows: “A graph G with p vertices and q edges is said to have Skolem difference Fibonacci mean labelling if it is possible to label the vertices x V with distinct elements f(x) from the set {1,2,...,F_p+q}  in such a way that the edge e = uv is labelled with  if  is even and  if  is odd and the resulting edge labels are distinct and are from {F₁, F₂,...,F_q}. A graph that admits Skolem difference Fibonacci mean labelling is called a Skolem difference Fibonacci mean graph”. In this paper, we prove that path, star, bistar, B (m, n, k) and union of stars are Skolem difference Fibonacci mean graphs.