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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*(uv)=⌊ 2[ f(u)2+f(u)f(v)+f(v)2 ]3[ f(u)+f(v) ] ⌋, for all uv∈E(G), is bijective. A g...

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Bibliographic Details
Published in:Journal of physics. Conference series 2020-07, Vol.1597 (1), p.12033
Main Authors: Arockiaraj, S, Rajesh Kannan, A, Manivannan, P, Durai Baskar, A
Format: Article
Language:English
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Summary: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*(uv)=⌊ 2[ f(u)2+f(u)f(v)+f(v)2 ]3[ f(u)+f(v) ] ⌋, for all uv∈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 S1, the triangular snake graph Tn and the arbitrary subdivision of S3.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1597/1/012033