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On entire face irregularity strength of disjoint union of plane graphs

Abstract:

A face irregular entire k-labeling of a 2-connected plane graph G is a labeling of vertices, edges and faces of G with labels from the set {1,2,…,k} in such a way that for any two different faces their weights are distinct. The weight of a face under a k-labeling is the sum of labels carried by that face and all the edges and vertices incident with the face. The minimum k for which a plane graph G has a face irregular entire k-labeling is called the entire face irregularity strength. In this paper, we estimate the bounds of the entire face irregularity strength for disjoint union of multiple copies of a plane graph and prove the sharpness of the lower bound.