FCM labeling of some graphs and its line graph

A function f is called an F -centroidal mean labeling of a graph G ( V , E ) with p vertices and q edges if f : V ( G ) → {1, 2, 3, …, q + 1} is injective and the induced function g * : E ( G ) →{1, 2, 3, …, q } defined as g * ( u v ) = ⌊ 2 [ f ( u ) 2 + f ( u ) f ( v ) + f ( v ) 2 ] 3 [ f ( u ) + f ( v ) ] ⌋ , for all u v ∈ E ( G ) , is bijective. A graph that admits an F -centroidal mean labeling is called an F -centroidal mean graph. The line graph is one among the graph operations. In this paper, we try to analyse that the line graph operation preserves the F -centroidal mean property for the path P n , the cycle C n , the star graph S n , the complete graph K n , the graph P n o S 1 , the triangular snake graph T n and the arbitrary subdivision of S 3 .