Total Edge Fibonacci Irregular Labeling for Fan, Wheel and Umbrella Graph

S. Amutha and M. Uma Devi1

Assistant Professors, Department of Mathematics, Government Arts & Science College, Sivakasi – 626 124, INDIA.

ABSTRACT

A total edge Fibonacci irregular labeling f :V(G) U E(G) —> {1, 2,..., k}
of a graph G = (V, E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x’y’ their weights f(x) + f(xy) + f(y) and f( x' ) + f( x' y’) + f( y') are distinct Fibonacci numbers. The total edge Fibonacci irregularity strength, tefs(G), is defined as the minimum k for which G has a total edge Fibonacci irregular labeling. If a graph has a total edge Fibonacci irregular labeling, then it is called a total edge Fibonacci irregular graph.

In this paper, we determined the exact value of the total edge Fibonacci
irregularity strength of Fan graph Fn , double Fan graph DFn, umbrella graph U(n, m) and Wheel graph Wn.