Face Bimagic Mean Labeling of Herschel Graphs and Its Operations

Abstract

A bijection ϕ: V(G)→{1,2, . . . , |V(G)|} is called a (1,0,0)-F-face bimagic mean labeling (FBMML) of G if the induced face labeling ϕ*(f_i) = = = k₁ or k₂, constant. This work investigates the possibility of face bimagic mean labeling of a Herschel graph. Also, a study of face bimagic mean labeling during the process of fusion of vertices of degree 3 of a Herschel graph and the duplication of vertices by the edge of a Herschel graph is provided in this research paper.