Total Edge Lucas Irregular Labeling For Some Cycle Related Graphs

Research Article
Ponmoni A Navaneetha Krishnan S and Nagarajan A
Graph labeling, irregularity strength, total labeling, Edge irregular labeling, total edge irregularity strength, total edge irregular labeling.

Let G= (V, E) be a (p, q) – graph. A total edge Lucas irregular labeling f:V(G)UE(G)  → {1,2,3, … . ,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 Lucas numbers. The total edge Lucas irregularity strength, tels (G), is defined as the minimum K for which G has a total edge Lucas irregular labeling. In this paper, we prove that the graphs such as Cm @Pn,Cm@k1,n,Cm@2Pnand Cn⊙k1  admit the total edge Lucas irregular labeling.