On entire face irregularity strength of disjoint union of plane graphs

• Published in: Applied mathematics and computation Vol. 307; pp. 232 - 238
• Main Authors: Bača, Martin, Lascsáková, Marcela, Naseem, Maria, Semaničová-Feňovčíková, Andrea
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.08.2017
• Subjects: Entire face irregularity strength; Face irregular entire labeling; Irregular assignment; Irregularity strength; Face irregular entire labeling; Irregularity strength; Irregular assignment; Entire face irregularity strength
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2017.02.051

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.