FCM labeling of some graphs and its line graph
S. Xavier Arockiaraj, A. Rajesh Kannan, P. Manivannan, A. Durai Baskar · Journal of Physics Conference Series · 2020
Abstract 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 Pn , the cycle Cn , the star graph Sn , the complete graph Kn , the graph Pn o S 1, the triangular snake graph Tn and the arbitrary subdivision of S 3.